I think in a world where you have talking swords, and guys in robes and funny hats who can wave their hands, throw a bit of bat guano in the air, and mutter some cryptic words and blow up an army of trained soldiers in armor, or turn the biggest, toughest dude on the block into a toad, the genetics of crossbreeding should really be the least of our concerns as DMs.
I do put some limits, but even major ones like half-dragon/weretigers or something, I'd allow....half-dragons happen not because someone had relations with a 50' long reptile, but because that reptile could use magic to assume human form, in which those relations are possible. The child could, theoretically, become a lycanthrope, through infection by a virus. It's like saying that a half-dragon can't catch pneumonia.
Some others, like half-illithids, I don't allow, because they don't jive with my perception of how illithids are born in the first place (ie. implantation of a tadpole in a helpless prisoner).
In any case, I find most of my players never select these kinds of characters anyways. Maybe my players are boring, but most of them are playing humans, elves, and dwarves. That's it. One of them kept trying new races, but even there, it was things like ghost elves, dryads, illumians, etc....no half-breeds.
Banshee