On the other hand, 'obligate' is a strong word to use for things as complicated as human behavior.

Specifically, there are gay men who are repulsed by the prospect of sex with women, and then gay men who are simply not interested (or not as interested) in sex with women.* It seems to me that 'obligate' is meant to refer to the first cluster, and should have a reproductive penalty roughly the same as male asexuality. (Figuring out what percentage of the population falls into that cluster is hard, since you can't really go off self-reports of preference; you want self-reports of anti-preference.)

*Straight men can consider how they would feel about having sex with another man; for some, there's a visceral disgust reaction, and for some there's just a "but... why would I do that?" reaction or a "eh, any port in a storm" reaction.

Knowing several older male homsexuals with biological children via socially-imposed marriage customs, I don't think the effect is as large as many assume under many environments.

In farming societies where monogamy is the norm and marriages are economic arrangements, it seems to me that the reproductive cost of sexual interest in men is minor (or possibly positive, if men in power are willing to trade resources for sexual favors).

But in societies where polygamy is the norm and men compete for women, it seems likely to me that any man who is less interested in winning is less likely to win, and the costs of sexual interest in men might grow significantly.