I've never liked Bethany much. I've met two and don't like either one, so that doesn't help.
Bethany can come off as super religious, but it doesn't have to. I think the combo makes a big difference; I'd assume Bethany Faith was quite religious, but not Bethany Autumn, for example.
The adult Bethany I know is always called Bethany, as far as I can tell, but the little one is usually called Bethie. That's her family's choice, though. I think Beth is mostly, but not completely, avoidable with Bethany. For some reason, it's easier for me to imagine an Elizabeth completely avoiding Beth than it is a Bethany, perhaps because Elizabeth has more options.