Yuri, as in... Love between two women? As in... Lesbianism?
Well. This is gonna open a can of worms if this topic takes off, but, welp, here I go. *Puts on miner's helmet with a flashlight on it, turns it on* Lets get to it.
RPG's De Facto Standards
Technically the one rule to rule them all is be "Fonz cool." Homosexuality of all forms is Fonz cool so long as it does not break the PG-13 barrier. If anyone tells you otherwise, they obviously don't know site policy. Generally speaking...
For RP's: It's on an RP-to-RP basis and up to the GM. If a GM rejects your character because they're homosexual, that's incredible uncool, but I guarantee you there's nine more GM's who will take it arms open wide in welcome.
For Staff: They don't discriminate, and there are no policies that reject homosexuality of any form. Not even the Yuri genre.
Personally: I have no problems whatsoever with the Yuri genre so long as it remains, strictly, in one of two categories.
A. (If underaged): It's written specifically for women of that age group to either fulfill a niché (that isn't porn), to educate, to give relate-able characters to the sexually confused, etc. (If it's NOT underaged): That it's not poorly disguised ecchi or pornographic content.
B. It's merely a de facto standard of the universe (or a bucking thereof), and is written to question the nature of sexuality, to enhance a character, to add a little variety to the typical homogenous hive-mind of heterosexual adventurers, etc.
If you're going to write homosexuality of any kind just for the sake of pornography or sexual entertainment? Here on RPG? You can go fuck yourself in my books. That's a waste of space, and time, and depending on how it's done, literally offensive to everyone reading it (both heterosexual and homosexual). If you're writing a homosexual set of character(s) (IE: The entire Yuri genre) for the purposes of showing that a homosexual is just as normal as everyone else, for additional flavour to an otherwise regular character, to help define a character's sense of self, to alter their interactions with other characters, etc, that's cool.
tl;dr: The Yuri genre is just fine on RPG. So long as it's not pornographic in nature.