Do non-frum who identify as Kohanim have a chazaka as being a Kohein? Is it relevant if the family wasn’t frum for many generations? If one of them becomes frum can he assume being a Kohein?
I don’t know where the story comes from, but it is said that the Gra, who was a b’chor, used to be podeh himself from every Kohein he met, until after he met a Kohein named Rappaport whose yichus he trusted and he stopped being podeh himself after that.
I heard one proof, FWIW, is to see the gravestones of ancestors. Does it say cohain in Hebrew? There still could some Yichus problems, like gerusha or chalutza, but at least there is something to start with.
Some people have real “Kohen” type names but are not Kohanim as sometimes in our history women couldn’t marry legally and stayed with their maiden names.