Lots of people define those things as what they're not. Usually in the form, "I am, you're not." It's hard (probably impossible) to define them as what they are. (I'm sure there are more, these were just the first ones I came up with.)
Point is, there are things the state should have a say in, and things they shouldn't.
Who owes what in taxes? State issue.
Who is allowed to have sex with which other consenting adults? Not a state issue.
What is the legal age for voting? State issue.
How many times a day do you bow toward Mecca? Not a state issue.
Who gets to self-identify as male, female, trans-gendered, married, single, black, white, Asian, Catholic, Baptist ... What difference do any of those things make to the state? You shouldn't tax someone more or less because they're Catholic. You shouldn't grant or deny the right to be an insurance beneficiary because someone is male, female or "other".
"Marriage" is a recognized ceremony in most major religions. If there's one where it isn't I'm not aware of it. That pre-dates any currently-extant law by quite a few centuries.
WHICH religion should then get to define marriage? "Oh no, I want all three of my wives to be able to visit me in hospital. Oh, and to get the tax benefits of marriage, of course!"You seem to be missing a pretty key point here. By reserving the word "marriage" to strictly religious use, the state isn't allowed to base visitation or tax laws on who is or isn't married. That would make as much sense as basing visitation or tax laws on who self-identifies as Baptist.