It's a practice of the Anglican church to do so for our own clergy. It's not a doctrine necessary to recognise other churches as apostolically succeeded. It is how most Anglicans view apostolic succession, but on paper we have a bit more flexibility, as with almost everything.
Anglicanism has not, to my knowledge, ever declared ‘invalid’ the Orders or sacraments of non-episcopal Protestant bodies. By taking communion in an Anglican parish, there is no implied condemnation of your Baptist family or upbringing. I would not spend a lot of time worrying about things like ‘apostolic succession’ or ‘sacramental validity’, important though they are. Getting to know the Prayer Book, specifically the Daily Offices, the Communion service, and the Church’s Calendar, is the most important thing you can do at this point, in the process of exploring whether or not you want to be Anglican. The main thing that will take some getting used to, is the relative formalism of our Services in the use of written prayers. The next biggest thing is the Anglican approach to Scripture. The Puritans who opposed the Church of the England believed that everything should have a positive biblical warrant; the Church of England’s position was that Scripture was the ‘source’ and ‘rule’ of faith, meaning that faith and practice could not outright contradict that rule. For this reason, the Church of England retained many things in her worship which had no positive biblical warrant, but which did not contradict the Scriptures, either (e.g., marriage rings, the sign of the Cross in baptism, etc.). I dare say more ink was spilled in the first hundred years after the accession of Elizabeth on these two issues than on any other, and they will be what you will most likely spend the most amount of time working through personally, since Baptists in America have tended to inherit the Puritan viewpoint on these things. Hope this helps.
If you mean, could we potentially recognize some Evangelical church as having apostolic succession, then no that wouldn’t be possible. At least hasn’t been the practice in the historic Church of England, the American Church, or any official Anglican capacities such as the Lambeth Conferences. Sure it is, in the 1662 Ordinal, and Article XXIII. “Of Ministering in the Congregation.” It is not lawful for any man to take upon him the Office of publick Preaching, or Ministering the Sacraments in the Congregation, before he be lawfully Called and sent to execute the same: and those we ought to judge lawfully called & sent, which be chosen & called to this work by men who have publick Authority given unto them in the Congregation, to call and send Ministers into the Lord’s Vineyard. That doesn’t mean the Baptist minister is bad and the RC one is good. But what it does say is, one can only be ordained by someone who is already ordained. Which is apostolic succession. It is a natural principle, not a supernatural one; there is no mysticism attached to it. One doesn’t get any extra goodness from being “descended from the apostles” and many lay people can be of more worth, and do better good for the Church, than someone who is ordained. The deification of priests as in the RC church has no role here. All apostolic succession says is, by the sheer logic and natural reasoning, “ordination can only be given by someone who first already has it”. You can’t just get a bunch of your buddies to “ordain” you, as has been the pattern in Evangelical churches. That’s all it’s saying.
You've hit at the most significant difference between the Anglican understanding of the call and the eccentric opinion that dominates confessional Lutheranism. In their thinking the call most originate from a local congregation and the office of the ministry acts to confirm the individual call. This system is beginning to not work so well as the confessional seminaries graduate increasingly more candidates than there are churches willing to hire them. These candidates are then left high and dry with ever decreasing chances of getting that essential first call the more years they enter the pool after graduation. Yet these men have, in effect, completed the proving year of diaconal service through the vicarage year. Still they wind up truck driving, teaching at parochial schools, or selling Thrivent financial products.
This is a general problem among seminary graduates, actually. The supply of MDIVs and MACCs vastly exceeds current demand. We are experiencing a glut of credentials in a market that increasingly is based off skills and relationships rather than credentials. The credentialism problem has exploded in the secular academic world. Secular universities still graduate loads of PhD astronomers, philosophers, and historians who will end up stocking shelves at Wal-Mart because their skillsets are completely misaligned with the current job market. (And spending their entire adult lives trying to pay off their $150K in student loans.) The scramble for tenured jobs in the academy is now a blood sport. Adjunct professors labor for years, sometimes decades, wandering like nomads from school to school, praying for the merest possibility of getting a tenured position. Adjuncts have become the helot class of academia (along with grad students). It's an amazingly feudal and abusive system, and quite shocking when you compare the actual behavior of universities with the "diversitarian" religion they profess. I'm of the opinion that half (or even 75%) of seminaries should just fold up their tents and close down. There are plenty of ways to offer online courses for a minimal fee that would give most people all the training they need for effective ministry, and churches can cover the "distinctives" with adult education courses themselves. We have a sufficient number of egghead theologians and expositors and commentary-writers. What we need are missionaries, evangelists, teachers, and apologists. As Christian witness in the modern culture continues to shrink, the need for cultural engagement and outreach increases. Willing hands and a believing heart are all the credentials a believer needs to start in ministry. Not everyone is called to be a great preacher or a member of the clergy. Much good can be done simply by organizing food kitchens for the homeless, helping set up bible-camps for kids, or handing out free bibles to strangers on the street. We need Christian musicians and artists and poets who can have an impact on the popular culture. Christians really need to lose this notion that the only "real" way to serve in Church is to be in the clergy. Lay ministry and mission work is the face our churches present to the world. Evangelism is something every Christian should do, not just the guy wearing a collar.
I think we have to be very careful here about what the Article is saying and what it isn't saying. Here is an excerpt (consisting, believe it or not, of only two sentences) from Bishop Burnet's commentary on Art. 23: In other words, the prevailing strict construction of the Article during and after when it was written, and what was taught in seminaries for centuries afterward, was that it was not saying that episcopal ordination was absolutely necessary for a given body of Christians to be a 'true church' (which would have excluded the Lutheran and Continental Reformed churches at that time). There is plenty of documentary evidence - including official diplomatic letters from Queen Elizabeth herself - that shows that this was about the last thing on anyone's mind at the time. There is no good reason for a layperson considering Anglicanism to be unduly worried about this subject. If one is more "Catholic" minded and places great importance on the actual, historical line of ordination of bishops, we have it (whether the Pope says we do or not). If one is more "Protestant" minded and does not wish to subscribe to any sweeping statements about churches with non-episcopal Orders, Anglicanism takes no such position itself and does not require that any of its members do so.
"True church" is not what I'm addressing, I'm only addressing "ordained ministry". Burnet is also a latitudinarian, not a hardline Anglican traditionalist, so that's an important deficiency for his Commentaries as compared to a dozen other influential Commentaries on the Articles that were written during the last 400 years.
The ordained ministry doesn't equal "The Church" right? On a desert island you can have "The Church" but not have any ministers. That's the distinction I am making. The question of apostolic succession only deals with the question of who counts as a valid minister. It has nothing to say about what counts as the True Church. That's a different topic. If a bunch of people came together to ordain Joe Sixpack behind the woodshed, an Anglican simply would not count that as ordained ministry. That's all I'm saying. There are no prevarications or qualifications on that point.
Can a church have true sacraments without valid ministers, in your view? I think that's where the proverbial rubber meets the road here. Valid ministry or not, Art. 23 is not denying that non-episcopal churches have effective ministry. "True churches" means they have sacraments, ministers, etc., i.e., everything necessary in order to carry out all the functions of the Church, even if their structure and derivation may be "imperfect".
I've always understood that Article XXVI stipulates that the sacraments, honestly received, are still valid even if they were administered wrongly or in bad faith.
I understand your point, though -- I would refuse to accept the wafer of the Lord's Supper from anyone but an ordained Anglican priest or bishop.
Private opinions are one thing, but what I’m talking about is just what is/was/has been the historic Anglican position. Anglicans in exile on the continent during Mary’s reign, for example, had no problem communicating with their Reformed counterparts. The Queen, the Supreme Governor of the Church of England herself, takes communion at a Presbyterian church whenever she attends Services in Scotland. The Hanoverians, in addition to being simultaneously Anglican and Presbyterian, were also Lutheran, and took communion in Lutheran churches when visiting their homeland. The OP is a young person considering Anglicanism, and I think it’s important she not be misled about just what ‘official’ Anglican teaching is.
You keep moving the mileposts. It doesn't matter what people do in other denominations, because the OP asked, what are the rules within Anglicanism. You're not going to be able to assert that the Reformed ministers are accepted as valid within Anglicanism, because if a Presbyterian minister transfers to us, we will ask him to be ordained; whereas if it's an RC one, we will merely ask him to make a profession of faith and be received. That doesn't mean the Presbyterian minister is worse, but it does mean that as bad as the RC one may be, he was ordained by people who were already ordained. In the worst case he would be a 'bad ordained minister'. Whereas as good as the Presbyterian minister may be, we judge that he was ordained by laymen, and therefore is not himself ordained either. He would be 'a good layman'. And just because the RC one was ordained validly, does not mean he is safe for a Christian to adhere to. There are grave questions about whether the Roman church uniformly professes the gospel. So the RC priest might be 'valid' but he will not be 'safe' or 'good'. We definitely don't believe that the RC church is 'better'. They just follow this one rule better, even if they may follow a hundred other rules worse.
The OP’s question was: Answering her question does not constitute moving the goalposts. On the contrary, you appear to keep trying to make the Anglican formularies say what they specifically do not say, viz., that apostolic succession in the episcopacy is essential to the Church. Neither the Church of England, nor Anglicanism in general, as I and others here have pointed out repeatedly, have ever taught this. That the Church of England has (usually) required reordination for ministers from some denominations is a matter of discipline, not doctrine.