Yeah, I'd say this is entirely up to the DM and campaign setting -culture by culture.
Are they "blessed/touched by the gods?" Or are they actual direct genetic descendants of gods/celestials/angels? Are angels walking around the world...and if they do, is mating with mortals something they do or is condoned at all?
Do people believe that even possible or are they believed to be actually half-demons/cambions in sheep's clothing? Are they shameful half-breeds of repugnant, "inhuman," ancestry...or exalted paragons of the potential of human goodness and perfection?
Or is your game/group/DM/campaign world just a melting pot hodge-podge kitchen sink where "everyone/every- species is special, so no one is" and you can find all peoples within a single city. So, no one blinks twice if you have horns or pointy ears or a tail or glow or feathered wings or polka-dotted-skin or white eyes or walk around with a head ringed with a flaming halo, glittering stars or green hellfire...shrug.
Is human society "Wow! Look! Is that a real elf?!" or "A beardless dwarf, purple minotaur, and hovering half-angel walk into a bar... and, oh look, they have a human with them, too! How very odd and original."
Aasimar can be ANY of the above, within a society...and any of these OTHER things to individuals or organizations or religions WITHIN that society.
There is no "X species is Y in Z society" in D&D. It is up to the campaign setting/world you are in and DM's detail of such matters.