One thing that I find key to understanding Anglicanism historically is the Elizabethan Settlement. As others have mentioned, theology is left vague *by design*.
The beginnings of that come from understanding that lot of blood was shed under King Henry VIII and his son and successor, King Edward IV, trying to change the Church of England from essentially a Roman Catholic Church to an essentially Protestant one (Edward IV in particular really went "low church" with an especially Protestant theology and practice) and then Queen Mary, Henry's daughter with his first wife Catherine, taking the thrown and restoring unity with Rome and shedding so much Protestant blood in making the Church of England Roman Catholic again that she is known to history as Bloody Mary.
So, here comes Queen Elizabeth I, the daughter of King Henry VIII and his second wife, Ann Boleyn, a Protestant. Queen Elizabeth had just inherited a Church of England and a nation that was Roman Catholic again and had gone through not one, but two, bloody changes in religious faith. However, her mother was Protestant and she was Protestant, and the people who helped keep her safe and would keep her safe and keep her in power at the beginning of her reign were Protestant.
Adding to the tension, you had Mary Queen of Scotland (Not the same person as the Queen Mary who preceeded Queen Elizabeth), who was Roman Catholic, and who had a tenuous claim to the British thrown. There were plenty of would-be revolutionaries instead and outside of England (Including, obviously, most Roman Catholic countries) who saw this Scottish Queen Mary as the true Queen of England, or someone who potentially could be if Elizabeth were killed before she produced an heir. Now, as we know, history records Queen Elizabeth as The Virgin Queen. Whether she was or was not a virgin is not really known (Some think she may have had an informal secret concubine), but also not really relevant, because for her off-spring to top Mary Queen of Scots in the line of succession, Elizabeth would have to have a *legitimate* child, which in those days was defined by a child inside of marriage, which meant she needed to marry to do this, and she refused to.
So, Queen Elizabeth, even though she eventually became very popular, reigned a long time, and is considered by history and the British people to be one of England's greatest monarchs, upon first coming to power and in her early years was balancing on a tightrope. She needed to stay alive, of course, first and foremost, and by both the nature of who she'd need to stay alive and her own family history and beliefs, was probably going to have to separate the Church in England from Rome *again*, making it the third switch from Roman Catholic to not Roman Catholic in four monarchies.
The question then became, how to do this without leaving a lot of the country, who were Catholic, plotting against her for the rest of what might have been extremely short stay on the thrown? And, further, how could she placate the Catholics without alienating her Protestant supporters?
Obviously, the most ardent Roman Catholics were not going to accept anything short of full union with Rome and the most ardent Puritan Protestants were not going to accept anything short of getting rid of bishops, crosses, the liturgical calendar, dancing, theater, etc.. *However*, there were, I think she must have felt, and been correct about, a broad swath of people in between- people who kind of wished they had unity with Rome, but could accept not being in union with Rome if they could keep Apostolic Succession, a three-fold ministry of bishops, priests, and deacons, a liturgical calendar with some important feast days and seasons, etc. on the Catholic side, and people who could accept some Catholic trappings and organizational structures on the Protestant side as long as they didn't have to be aligned with the Pope and could have masses in the vernacular (English in England, as opposed to the Latin Roman Catholic masses of the time), mass printings of bibles that people were encouraged to own and read, etc..
So, the thinking was, okay, get the people in the middle on both sides, and you can stabilize the nation and the church, and only have to deal with uprisings and plots from the fringes, and that's basically what she did. She separated from Rome and had perhaps the most Catholic Protestant church or the most Protestant Catholic church in the world at the time. Part of this was by having some things be planted firmly in the middle, and part of it was by trading some things from one side for some things on the other side, but most of it was by basically allowing for enough vagueness in theology that people could kind of be mostly Catholic without the Pope or mostly Protestant with a few extra traditions and organizational habits, and each side could see things their own way and come around a common table for communion on Sunday.
This wasn't a formal document, but essentially it's what's known as the Elizabethan Settlement, which sounds very formal, but is really just a concept. The church was known as Protestant in terms of the politics of Europe, but was pretty open to people who'd have not passed as Protestant in continental European Protestant countries.
Or, to put it more theologically, it's the philosophy of "both, and" or, as the saying goes, commonly attributed to St. Augustine of Hippo (But actually likely to have originated later), "Unity in the Essentials, liberty in the non-essentials, in all things charity".
Saying "Real Presence" and leaving it at that while specifically ruling out transubstantiation and memorialism was not unintentionally vague, it was intentionally vague. It let everyone believe what they wanted to believe- to a point.
Now, as we go forward some years, there is the Anglo-Catholic/Oxford movement of the 19th century to restore Catholic elements that were deemed lost or not recognized enough, and there is this large international Anglican Communion made up of self-governing national churches that each set their own theology and practice, and you've got a via media (middle way) between liberals and conservatives too as well as Anglo-Catholics and Evangelicals and High Church and Low Church.
So, the differences grow even broader.
And, of course, most national churches are simply not bound by the Protestant leaning 39 Articles any more than they are bound by it's more Catholic predecessors. In the US Episcopal Church, it is now considered a historical document, and that's it, not a profession of the faith of every Episcopalian.
And in this forum, you will also find a lot of people who are members of churches that are Anglican by tradition, but are not in the Anglican Communion that the Church of England and the Archbishop of Canterbury are in, and who split for various reasons.
So, the answer to your question depends on a wide variety of factors. You would probably be welcome as a member of most of these churches believing whatever you wanted as long as it somehow fit in with the words "real presence" and involved a reverence for the sacrament in practice during Eucharist services. Some Anglo-Catholics are now even explicitly embracing transubstantiation.
I think the idea is that if you want marching orders, you're not going to get them in most official Anglican provinces except in select areas of the world like Africa. If you want a church that gives you form and substance but respects differences and asks people with some differences to all come together at a common table and share communion together showing that same respect to each other, you might well like most Anglican churches (And of course one may find a particular parish that leans more one's way to attend in one's area than some other parishes).
But if you want the Anglican stance on [fill in the blank], you almost always are going to get back a vague answer that is indicative of a wide range of acceptable responses, but that does perhaps rule out one or two possibilities.
That's the point. It's supposed to be that way. I know that comes as a foreign concept to people who may have grown up in a tradition that told them they need exact precise answers to everything and must all agree on them or else face the consequences, but you are asking about a different church than whatever you attend or grew up with, so you can expect some foreign concepts.
Around the time of Vatican II, it was widely expected that Anglicanism would be the ecumenical bridge that brought Roman Catholicism and the Protestant churches and denominations together. Then Rome went right, and some Anglican provinces went left, and, well, that's probably not going to happen anytime soon. But, essentially, theological vagueness to some degree can be viewed as a strength and not a weakness of Anglicanism.
I also have to say, in modern times, there is something to be said for people who sometimes go back and forth a little bit between feeling Catholic and Protestant, or progressive versus conservative, or high church versus low-church, not having to switch churches every time they wake up on a different side of the bed.
You just find a parish and go and take communion on Sunday. If it starts to bother you because it leans this way or that and you want a break, take a longer drive and go to another nearby parish that leans a little bit the other way. And it's all the same structure under the same bishops and dioceses and national church structures, with the same prayer book across each nation all based at least loosely on the first English BCP, and all in communion with each other (Well, all the ones that are in the Anglican Communion- not the breakaway churches that keep the name and not the affiliation, obviously). I think that's one way of looking at this tradition, anyhow.
