Some religious leaders insist that believers should have the right to discriminate against others, because of what the believers believe. For example, a hotel owner might want to ban same-sex couples based on their belief that same-sex relationships are immoral.

One aspect of this sort of situation that I have not come across before, and an additional argument in favour of equality, is that the state should not get into arbitrating religious disputes. It's well known that there are religious people who are gay and who believe that their sexual orientation is not a problem for their religion. Now, what happens if a religious same-sex couple gets refused entrance to a hotel by religious owners? If the state should support the religious rights of believers, then which of these believers should the state support? It can't just pick the majority view of the religion as that's clearly unfair. The only fair course of action for the state to take is to consider the situation without taking religion into account, and arbitrate one way or another based on secular considerations.

Insisting that believers should have the right to discriminate is not just unfair to those unbelievers who may be discriminated against - it's also prejudiced against some believers. Only by acting in a secular way can the state resolve things fairly.