From a legal standpoint, this isn’t actually all that slippery.
Can both parties consent? Can they sign contracts? No? Then they can’t marry. The legal definition of consent means that inter-species and marriage of children are and will continue to remain illegal (barring change of the consent definition, of course), because they cannot legally consent nor sign contracts.
Incestual marriages get a little slipperier, since two adults can still consent. However, that’s still enough of a cultural taboo that it’s not likely to be addressed (and the subsequent laws explicitly banning it repealed) and come out of the realm of fringe anytime soon. The ins and outs of it are also a discussion unto itself, and out of scope for this particular conversation. For now, I’ll concede that this is a route that could technically be pursued.
From a moral standpoint? It’s pretty simple to me — if you don’t approve or think it’s immoral, don’t partake, and teach your kids to not partake. Think same-sex marriage is immoral? Don’t marry someone of the same sex as you. Think inter-species relations are immoral? Don’t practice bestiality. Think incest is immoral? Don’t have sexual relations with your relative.
And what if someone else is doing something you consider immoral? Ask yourself this — are they, or have they, infringed on another person’s rights? Are they objectively harming themselves or others? Do they objectively threaten your safety? No? Then why are you so worried about what they are doing?
More concretely — if you consider gay marriage immoral, ask yourself this: how does Joe and Bob’s marriage affect your own? (Hint: it doesn’t.) If you consider trans to be immoral, ask yourself: how does Mattie being trans affect you? (Hint: unless you two have an intimate relationship with one another, it doesn’t.)
You may not like what someone else is doing, and you can choose to continue (or not) whatever relationship you have with that person, but it’s not your place to push your morals on someone else.