Yes, any business should be able to deny service for any reason

if the person is being rude or harassing other customers/employees then they should provide no service but religion should not matter at all.

Business owners can not use religion as a reason to refuse service because not everyone falls under the same religion so there's no reason they should be held to that religion's standards. For example, a Christian business owner may oppose gay marriage due to their religion, but a gay customer should not be penalized for not adhering to the owner's beliefs.