Before puberty, identification with a sexual orientation would have to be completely socially constructed, so in a gay-friendly society most people should identify as bisexual by default.

This is not the case. Many gay people know that they are gay at a young age, often well before puberty. Or they realize that they are somehow different from the others around them. Human sexuality is not as simple as an on-off switch with the whole system coming into play when people hit puberty.