Where an issue of religion (or ideology) comes into play is in terms of commerce - the duty to engage in actions you think are evil if you want to participate in the economic system.
For example, the lawsuit against the baker who wouldn't do a cake for a gay wedding. That would be an example of the OP's topic.
Is it political correctness being now required and contrary to beliefs? Although obscure, there are religions that have racial aspects. If you had a business making signs and someone wanted a bunch of KKK and racists signs saying "N....ers Are Demons" - could you refuse? And if you did, isn't that religious discrimination?