It's not all about methodology. It's about a fundamental belief that some people hold that "you're wrong and I'm right" coupled with "and I get to impose my values and beliefs on you."

I make no claim to absolute knowledge about the existence of any gods nor to the correctness of any one religion, or none. I don't impose my values on others, but simply ask them to not impose theirs on me.

An obvious example is same-sex marriage. If you believe your god abhors it, then don't marry someone of the same sex, but also don't tell me that I cannot and try to establish laws to that end. Someone else being gay or married to a partner of the same sex doesn't harm or threaten me in the least, nor does it threaten society. So what's the problem?

In most cases, it's the religion that's driving the politics, not the other way around. Believe what you want, practice how you wish, and leave everyone else the hell alone to do the same.