I don't want to hand out religious themed christmas cards at work
Why don't you want to hand out religious themed Christmas cards?
I don't think it's a appropriate to do so.
It's understandable that you wouldn't want to hand out religious theme cards if you're not religious, but you should be respectful of other peoples beliefs. If your coworkers are religious, then there's nothing wrong with handing out religious themed Christmas cards especially if it will make them happy.
I'm worried they will judge me.
Maybe you can just talk to them and explain why you feel this way.