Disclaimer: I have not actually played Shin Megami Tensei: Persona 4, but I have seen it played for 60-odd hours, which naturally included most of the story elements.
Persona 4 has the potential to be a wonderful game from a queer perspective, as it raises interesting questions about masculinity, femininity, homosexuality, and trans* issues. It's set in a high school and town in Japan and features a cast of eight main characters. The characters who are most interesting in light of these issues are Kanji Tatsumi and Naoto Shirogane. Kanji is a bad-ass who beats up bike gangs and gets hassled by cops because of his attitude. He also loves sewing and crafts and is the heir to a textile shop (the fact that he got bullied for his love of crafts is also one reason why he started acting as a tough guy). In the sequence where the characters enter the Shadow World created by Kanji's psyche (the main conceit of the game is that we have shadow versions of ourselves representing parts of us that we don't accept, but over the top and distorted), it's in the form of a "hot bathhouse" and the shadow version of him is an over-the-top and lisping lad-fancier. He was also seen before your team enters his Shadow World in conversation with a boy (actually Naoto) that gets him rather flustered. At the end of the Kanji quest, Kanji accepts "that part" of himself, which I think most people would interpret as him accepting his homosexuality.
The problem Kanji's storyline (apart from the over-the-top bathhouse imagery, but that could be ok) is that very little is said straight out, and not in the good way. It might just be a problem with the translation, to be sure, but I think the most common word when referring to Kanji possibly being gay is "strange" (the Japanese "hen"?) and homosexuality in general as "that thing". So the very thing is unspeakable to begin with, which doesn't really inspire confidence. This is aggravated by the other characters (especially Yosuke, but he is not rebutted by the others) pretty much making fun of him for being gay in a very heteronormative way, like at the School Culture Festival "date café" where it's suggested he should take the girls' side, and at the cross-dressing beauty pageant (which is soooooo funny), without actually saying straight out that he's gay. Being made fun of sets Kanji off, being a bit of a hothead, but it sets him off in the "I'm not gay and stop saying I am"-kind of way, because it starts being more and more clear that Kanji actually isn't. So for most of the game that includes Kanji, gay men are made fun of in a really trite manner and even when not made fun of outright, aggressively othered by both the other characters and Kanji himself, and the player is given little chance to rebut the idiocy.
The good part about Kanji's story is at least that he comes to terms with and starts taking greater pride in his love of crafts and creating wonderful stuffed animals and the like for the town's children, so at least standards of masculinity are questioned.
Now over to Naoto, who is at first presented as a boy (and a genius detective, bit of a Tintin thing going on), and is the one who makes Kanji flustered. In hir Shadow World, the part that zie needs to accept is the fact that zie is still a child on the one hand, and (big reveal!) that zie was born a girl on the other. After that reveal it's not entirely clear which way Naoto will go, as it also includes a line about accepting hir body the way it is (and implying that acting as a boy is because zie thought being a boy would make hir dream of becoming the best detective zie could be possible (which raises some interesting gender questions in itself). However, as the team goes back to school, Naoto still dresses as a boy and says that zie will go on much like zie had before. Now, however, the entire school is gossiping about how zie is actually a girl. The team proceeds to try to pair Naoto and Kanji together (which is ok), and making constant references to how Naoto is actually a girl, including the oh-so-sensitive "oh right, you're actually a girl, no wonder you got kidnapped and couldn't fight back" (never mind that bad boy Kanji got kidnapped far more easily) and comments about hir cuteness. At the School Culture Festival, there is also a "regular" (meaning, of course, one for girls) beauty pageant, where the girls of the team are signed up against their will, including Naoto, at which point I was in an apoplexy about the trans* and gay bullying going on in the game.
In Naoto's case, zie is still, at the point that I've so far seen of the game (about 4/5 in) a competent detective, but so far no mention of gender issues in conversations with hir. I sort of suspect that any lingering trans* issues will be erased as the game continues, though, and that the normative will be authoritatively restored to the school, thus utterly wasting some of the most interesting character setups in video games.