If they allow other religious-based clubs, they have to allow it. If they prohibit Bible clubs, then the will have to do that if they allow the ‘Satan’ club.
Only because of a false interpretation of the First Amendment. The First Amendment does not create a "wall of separation" between church and state. Nor does it require religious neutrality by the state. It reads:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof…First to be noted is that this only applies to Congress, not to the states. Second, it does not forbid laws establishing religion but rather laws regarding the establishing of religion or the free exercise thereof. Congress can pass no law forbidding a state from establishing a religion just as much as it cannot mandate it. In other words, what the First Amendment actually does is take the question of establishing a religion out of the Federal jurisdiction and reserves it to the states.