Relative to what? If "lots of things" are "relatively" something, your standards are probably too low.

Yes, twin studies give a simple upper bound to the genetic component of male homosexuality, but it is very low. As an exercise, you might try to name 10 things with a lower genetic contribution. But I think defining "innate" as "genetic" is a serious error, endemic in all discussions of human variety.

Added, months later: Cochran and Ewald suggest as a benchmark leprosy, generally considered an infection, not at all innate. Yet it has (MZ/DZ) twin concordance of 70/20. For something less exotic, TB is 50/20. That's higher than any reputable measure of the concordance of homosexuality. The best studies I know are surveys of twin registries: in Australia, there is a concordance of 40/10 for Kinsey 1+ and 20/0 for Kinsey 2+; in Sweden, 20/10 and 5/0.