One big difference is that no one wants to have incestual or beastial sex. People want to have gay sex. This usually comes up in gay marriage slippery slope arguments. If you legalized all three for marriage tomorrow, there'd be a ton of people getting married to people of their own gender but basically no one getting married to their sister or dog.
As for the moral question there's nothing wrong with incest. Beastiality is animal abuse based on laws of consent we already have established (and are really quite conservative, honestly 16 year olds are probably entirely capable of giving informed consent for sex).