"It is the combination of a set of religious beliefs and social teachings, with the attempt to implement those doctrines throughout the society by political means that characterizes the religious right."
Fair enough. What I take as the key is "attempt to implement those doctrines throughout the society".
On the other hand, any law is based on the concept of right vs. wrong, and that concept must have some underlying moral belief to it. Yeah, yeah, I get the whole utilitarian thing but the fact is that "greatest good" still requires that we define "good" and there you would be right back at Hume's Fork, having to make underlying moral decisions.
I think if members of religious groups insist that everyone in society should behave just as their religion demands people behave, then that's a problem. I personally feel however that if a religious group simply tries to influence the body politic with their views of right and wrong, they are doing no more than any other group, and no more than is their right and duty as citizens.
This being the case, if a person cannot stand these people, I don't see how it can be over their interest in influencing society to their way of thinking. Everyone does that. It seems to me at bottom, saying one "cannot stand" religious people of a certain political view pushing their agenda, can fairly be translated as "cannot stand religious people of a certain political view, period."
Now, I agree everyone has the right to not be able to stand the members of a group as a result of the group's views (though scripture admonishes Christians that this is a sin and Christians themselves should not fall into it). I think it's also important however to recognize this is no more than simple disdain for the group's views, and disdain for members of that group. The group doesn't have to do anything in particular to 'earn' this disdain other than, perhaps, advocate and vote according to their principles.