Not having to worry about it, not being aware of it, and not being affected by it negatively.
Religious privilege is being able to boil down "religious privilege" to "ooh, you're upset about some words on the dollar bill? Pick your battles."
Assuming that when you ask people to bow their heads and pray, that everyone will and no one would have a problemw ith it.
Assuming that when an invocation is given before a football game or town hall meeting or meeting at work, that it's welcome by everyone in attendance
Knowing that the basic tenants of your religious beliefs are codified into law, and that they are well-represented by all members of government, from dog-catcher to president to supreme court, and everyone in between.
Never having to think about whether it's offensive to tell someone you're praying for them. Never having to think about asking someone what Church they go to. Never having to wonder whether it's okay to tell someone about how they can become born-again, or saved.
Never worrying about being allowed days off during your high holidays. Never having to assume that your major holidays won't be given a preference for Federal and State holidays.
Nope. Religious privilege means willfully ignoring or just being ignorant of the above, and boiling it all down to people being mad about "In God We Trust" on our money.
That's what religious privilege is.