Yeah, this touches on a number of points that have (afaik) been going around in LGBTQ discourse since the '90s, at least--the problem of how, exactly, to define the "gay" or "queer" experience. Or, in another phrase, "How queer is queer?" It can get pretty divisive; I've seen people accuse Call Me By Your Name (!) of being "a gay movie for straight people" or suggest that it isn't "queer enough." An odd claim, from my perspective, but suggestive--the question is, is a movie "gay" just because it features two people of the same gender-identity falling in love? Does In & Out count as a "gay" movie? Does Rope? Certainly if I were to create a queer film canon I would include Rope and exclude In & Out, even though the latter has a character who openly says he's gay and the former does not, but what are the grounds of this distinction? Etc.
[EDIT: I'm sure you've encountered this book, but let me quickly plug In a Queer Time and Place, which runs through the above questions w/r/t the trans experience]
Put another way, Adams isn't talking about BR and "other gay movies"--he's suggesting that BR isn't a gay movie at all. I think Adams' critique is precisely the opposite to the issue you allude to in your second 'graph. The problem for Adams isn't that Freddie isn't "incidentally gay" but that he isn't gay enough. If I understand Adams' objection to Bohemian Rhapsody, it's that Freddie's queerness is pretty much incidental--so incidental that, when they brought the movie to China, it was possible to remove all of it with the excision of a couple of minutes--and that whatever queerness is shown is seen as a source of anxiety and depression (this is Adams' critique, not mine, since I've not seen BR, which I should have noted above). Which, when you're dealing with a character so obviously and deeply queer as Freddie Mercury, seems kind of an odd choice. The thing about having the "right gay voice" is that (again, by Adams' estimation) it allows Rocketman to get at some realities of gay life that might seem obvious from within but are often not obvious from without. This argument raises the specter of "authenticity," which I think is a red herring, but it also suggests one of the ways that having (for instance) a diverse writing-room can make a piece of art stronger or more interesting.
Now, as far as the larger scope of issues you bring up--yes, there's broad similarities between Christian film and LGBTQ film (up to and including the fact that most examples of both forms are, first, produced by members of the in-group and, second, pretty terrible). I do think we could make some important distinctions regarding why filmmakers from each group (insofar as they're separate groups; I'm uncomfortable with the implicit line between "Christian" and "gay" but I'm accepting it as a generic distinction as far as film goes) make their films. There is, as you note, a hunger for representation from each group, and the respective genres fill those needs. What I'm not sure of is the extent to which the question of evangelism comes up. Christian movies have a weird thing where they're kind-of-sort-of trying to "win souls" or whatever while at the same time "preaching to the choir" because, let's face it, it's mostly Christians watching these things. Meanwhile, a gay flick like John Apple Jack seems pretty uninterested in even pretending that straight audiences exist (I imagine the same could be said for the Eating Out series, but I've never seen them). [EDIT: There's also a question of audience-expectations. The audiences for God's Not Dead, based on my Facebook feed, seem to take a tremendous amount of pleasure in being told they're right, while the audiences for most gay movies--again, based on the discourse I see online--are happy to settle for being told they're valid. I wouldn't want to insist on this latter point too strongly, though, because my personal experience is limited and idiosyncratic.]
In fact, the only time a movie with queer themes starts considering a straight audience is when it's pitched to go big like Call Me By Your Name or Bohemian Rhapsody. There may be parallels here, too, in the way (for instance) Christian themes got rinsed out of the Narnia franchise, etc.
Anyway, sorry for the wall-o-text. Your comments just got me thinking.