Medievalists or students of Church history probably know what I'm talking about; for the rest of us, here's some links:
The one useful comment on this from a previous thread last year. There were other threads, even older or even smaller.
Wikipedia article on the so called medieval "same sex unions" that could or could not be romantic in nature.
That's an important debate on whether those ceremonies were fringe or accepted by the Church; and whether or not homosexuality has always been condemned in Christianity or if it was a later development. This may not seem like a biggie for non-Christians, but my layman speculation is that it's going to get relevant as LBGT-supporting churches get more numerous.
Also people just can't agree if Boswell wrote a reliable, academic book or not.
So, the main person who has argued that adelphopoiesis was a same-sex union (ie, a marriage-like union or even an outright marriage) was John Boswell, as you point out. The issue is not, as your title might imply, whether these ceremonies actually occurred (they did) but what they meant. And your question really seems to be, is Boswell's interpretation of adelphopoiesis as a type of marriage ceremony between two men accurate?
The simple answer is that, no, most scholars don't seem to take Boswell's arguments about adelphopoiesis seriously. It was certainly not a gay union which could be seen as a simple precursor to gay marriage today, and it's very misleading when people stumble upon the work and try to use it as proof that medieval gay marriages used to exist. The more complicated answer is that it may have had some homoerotic undertones, and may have had some connections with marriage liturgies, but we don't have a lot of primary sources on the issue (it was not a very common ceremony) and few scholars since Boswell have actually worked on it.
It may be useful to contextualize this within Boswell's work on gay and lesbian studies more generally. His major work, which came out in 1980, was Christianity, Social Tolerance, and Homosexuality (CSTH). It was a revolutionary book when it was published, and it was highly praised outside of academia (for example Time magazine helped popularize it). Within the academy, as well, it was well-received, but with more measured criticism as well. To boil the book down to what is sometimes known as "The Boswell Thesis", CSTH argues that the early church, and the church into the Middle Ages, was not particularly concerned with homosexuality, and that prohibitions against it did not start developing until quite late.
The Boswell thesis itself is more or less accepted by most historians. However, Boswell sometimes over-reached in his arguments. There is a central problem of talking about homosexuality in the pre-modern era, which is that the concept of the homosexual individual essentially did not exist before the nineteenth century (see our FAQ for more on that). Boswell himself admits this, but he argued that just because there was no word for gay/homosexual that that didn't mean there weren't homosexuals and that they couldn't be studied historically.
The problem with his approach, though, is that Boswell sometimes over-reached. Even is CSTH you can see that. He often re-translates Latin texts to say things like "the gays" when the Latin word should more accurately be something like "the youths", and he sometimes seems to be imagining much more homoerotic content than his sources actually prove or even imply.
This criticism doesn't invalidate all of Boswell's insight, of course, and CSTH is still one of the most important pieces of LGBT scholarship of the 20th century, arguably one of the most important pieces of medieval scholarship, and maybe even one of the most important pieces of historical scholarship in general. The scholars who have followed in his footsteps have been able to make many insights about gender and sexuality in the Middle Ages because he paved the way, and he was aware that much of what he originally wrote might be proved wrong as more eyes moved to the topic (one of the quotes that he put at the beginning of CSTH even seems to welcome that).
Unfortunately, Same-sex Unions in Pre-Modern Europe suffers from the same problems of over-reach as CSTH does, but perhaps even moreso. The trouble is, as I've alluded to, it's very hard to actually prove that there was any implication of marriage in the adelphopoiesis ceremony. It was perhaps more likely an adoption ceremony, or even a ceremony that two men would undertake in order to solidify their friendship (friendship is a very important social construct in the Middle Ages). There's really very little evidence that these ceremonies were intended to be at all like marriage ceremonies, and even less that the participants lived together as spouses. Certainly if they were quasi-marriages, the participants would probably be assumed to be sexually chaste. The larger issues come down to those of translation and interpretation. Many Byzantinists have found his linguistic arguments and translations lacking, and as he has (and we have) very little other evidence about the unions, that seems to be the main argument against the book. That said, there is still definitely a certain implication of homoeroticism in the ceremony, and it's quite possible that Boswell is at least somewhat correct. To give you a sense of the trouble that his detractors and defenders have making their points, read this review of a review by Paul Halsall. At one point, Halsall is literally defending Boswell by arguing that a mis-translation was really an accidental misconstrual, not a deliberate one.
You may wish to look at, in supplement to CSTH and Same-Sex Unions, the book The Boswell Thesis: Essays on Christianity, Social Tolerance, and Homosexuality, edited by Matthew Kuefler. I also have found Carolyn Dinshaw's essay from that volume online, and I would really recommend it if you want to get a sense of how impactful Boswell's work actually was, but also to understand Boswell's argument that we can find evidence of homosexuality in the past (an extension of the medieval debate between realists and nominalists!).
The ceremonies were definitely accepted by the Church - it's what they signified that's a matter of some debate, which isn't helped by the rather complicated concept that "homosexuality" (or even the idea of "sexual identity") is a really recent construct.
There's material on St. Theodore of Sykeon's brother-bonding with Thomas, patriarch of Constantinople, at the Fordham University Medieval Sourcebook. That's... pretty much at the center of Church acceptance, if you asked me. (This is before the East-West Schism.)
There's nothing to say they had a sexual relationship, though obviously from that record, they had a deep and loving bond.
Fordham also has a LGBTQ history page that's a few years old, but still a great collection of primary sources and debates over what they really mean.