I honestly don't see how gender identity matters AT ALL in the context of sports. The fact that he's admitted to feeling male doesn't change how he plays the game at all; he's still undergone the female socialization in high school, and knows how to play in the context of women's sports. Gender identity shouldn't come into play. As far as strength/endurance etc go, it's the hormones and the puberty development that will affect this, NOT the gender identity. If he chose to play and receive T therapy, yeah, he should be excluded solely for the fact that he's effectively using steroids. No athlete should receive this undue advantage, even if they're receiving the steroids for legitimate medical reasons.
Now for the female transthletes. We've been socialized in sports as male, and will probably play in a more masculine way; for better or for worse, that's how it is. I think that many (most?) of us are willing to disregard this, and that's fine. Maybe it doesn't play as large a role as I'd like to think. We cannot disregard the effects of male puberty though. I'm 6'4-6'9 (it varies by how my neck/back are that day.) I've undergone MALE puberty to grow as large as I have, and it's important to consider the effects that something like that might have on female sports. My T levels happen to be very low naturally (off topic, doesn't matter for this thread,) but I would still experience a significant benefit when it comes to sports in which size makes a difference (e.g basketball or swimming.) Even if I had an orchi, had estrogen etc for years, the benefits conferred by developing male won't be fully negated.