1. Black judges could not try cases involving civil rights. Nor could a judge who's a member of any minority. Of course it wouldn't stop there. Judges who are white couldn't try cases either, since they're not minorities, but rather, part of the "oppressive majority," as the argument goes. Everyone has a stake in the case, white and black.
2. Judges who are straight couldn't decide sexual orientation cases. After all, as the religious right keeps telling us, straight marriages are at risk. So any straight judge who is married, or contemplates possibly ever getting married, would have a personal interest in any gay marriage case, and we can't have that.
3. Female judges couldn't decide any case dealing with gender.
4. Meat eaters couldn't try cases against PETA. But then again, Vegans couldn't either.
5. And no Republicans or Democrats could ever try any political cases at all. So basically, no judge could ever try a case brought before it by the Congress or the executive branch.
If anything, the accusation that gay judges are per se unable to be fair and objective judges is prima facie evidence of the bigotry and animus motivating Prop 8 supporters.