>>18066421 (OP)
Depends.
-If we've had them forever then we'd have probably been stuck in the bronze-age for *EVEN LONGER*, given the inherit technologically stifling qualities of magical-people (and the anti-tech things they'd need to do to retain or continue producing magic-people like erecting large stones, growing big trees, preserving ?dragon populations?). Assuming we made it to modern times I would still expect these bronze-age imperial style cults to still exist as castes and important "living cultural artifacts", like how Japan still has their royal family. I also don't think anything resembling vague, faith-based, monotheistic religions, would have formed.
-If this is something that's *just happening right now* I think there'd be some amount of hysteria/societal anxiety as people try to rationalize or figure out how people get magic, how it works, etc.. Magical institutions, would need to be founded, the field of paranormal studies would have to be dramatically expanded and funded in order to study these people and any potential influence they have on ecology, physics, etc..
I don't think magical people would be "locked up and dissected" (in 1st world countries at least), but I do think they'd be people of interest strongly pressured into attending institutions and medical facilities to work out the mechanics.
DESU, either way I think it would be a lot like how Hinduism is in India. By that I mean constant filthy superstitious chaos. Information is too readily available nowadays, nobody can keep a secret. People would quickly figure out magic and you'd have millions of people rattling beads, performing bizarre rituals, erecting shrines and temples everywhere, there'd be a never-ending supply of unsuccessful magicians and two-bit sorcerers begging on the streets.