Non-Muslims are permitted to enter the Sheikh Zayed Mosque in the UAE (the only requirement is that they dress appropriately), and tourists from all backgrounds are welcome to visit the Hagia Sophia Mosque, formerly an Orthodox Church. I've been to both, and nothing weird happened.
Us Christians allow even non-believers to come to church because, really, a building isn't where God dwells and no one is perfect. It is just a building and kujifanya Deputy Jesus or Assistant Mohammed is where we go wrong.
People need to take a chill pill and learn to love people instead of bashing them for such flimsy reasons.