Strictly speaking I think the books tend to have a set list of animals paladins are allowed to summon as a mount, but apparently expanding the list of options is a common House rule… though I imagine many DMs learn to regret that eventually.
Frankly centaurs seem to be in a weird category where technically it’s not bestiality, I mean clearly they pass the Harkness test and all that, but it’s still going to weird people out. Even more than mermaids really. Perhaps because unlike mermaids, people actually understand exactly what the mechanics of sex with a centaur would involve.