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Ranczo lists this under Subculture of the Week (to be fair, the character in question changes both faiths and subcultures like gloves - with her airheaded mother and cynical father, well, she never had anything to fall back on) which seems a weak match, but I can't see anything better.
Closest thing would be Emergency Multifaith Prayer.
Good morning, and good night, I hardly ever sleep. With what I have, what else do you think I'd ever need?Desperately Seeking A Purpose In Life if they're actually trying to find something to give them direction and meaning
Egocentrically Religious in whiny form if they're expecting enlightenment to come as some grand revelation after a token effort and moving on when they don't get it, and/or in utilitarian form if they move on as soon as the doctrines of a faith inconvenience them.
Edited by Scorpion451

A character seeks experience with as many different faiths as possible to reach the some kind of spiritual enlightenment or truth