About the closest is probably Baha’i which argues strongly for the equality of the genders, with no social or spiritual subordination. Up to a point, that point being the glaring exception of the elected nine member ruling body, for which women are not eligible. They can hold every other senior administrative position except that one, the reasons for which were left entirely vague (“you’ll see guys, it will all make sense one day!”).
So I wouldn’t call it truly equal and it still has some conservative social holdovers you’re supposed to adhere to if you’re a member in terms of stuff like no pre-marital sex, booze, adultery (damnit!) and practicing homosexuality (though if you promise to stay celibate like all those unmarried folks should, they’ll give you a pass). Though they only have that opinion if you’re trying to be a practicing Baha’i - folks outside the faith can do whatever. As they are also explicitly supposed to stay out of politics, you’ll at least never see them trying to legislate their “family values”-style moral stances.
Other than that with their emphasis on universal equality and respect for all other religious faiths they’re probably as doctrinally “liberal” as Abrahamic religions are gonna get. Still not 100% equal though.