It's a fine line.
Is there a state religion? No. (technically)
Do "Christian" politicians use the fact that they can whip their constituents into a frenzy simply because the oppnent is either not as vocal about their religion, or even worse, feel as if religion is being imposed in the government? Yes. In that case, a de facto religious influence is being introduced.
When religious/Christian precepts are introduced as law, to be legally binding on all, even those who don't believe in it, then we have a problem. It should be obviously a case by case discussion. But Christian political interests are primarily social politics. Instead of being "live and let live" social political discussions do demonize minorities and their rights, under the auspices of "morality".
A democracy is only as strong as their commitment to the protection of minority rights. When the majority insists that their rights are being infrigned upon, I find that a bit disingenuous, and I do see that from the Christian right that tries to thrust themselves into the public social debates.
Christians are allowed to feel strongly about whatever they want, and limit it to churches and their families. They simply cannot be permitted to introduce as potential law anything that seeks to limit the rights of others due to the simple fact that their religious sensabilities are offended.
If for example, someone only subscribes personally to 8 of the 10 commandments, an allowing of all 10 commandments in a government building would make me feel quite uncomfortable, as I reject 2 of them. Why should all 10 be thrust upon me as a secular political ideal? Ditto if it were only 4 or 5, 2 or 1.
I see this issue as a continual weakness in our democracy. Until religion is kept out of the public discourse, we will continue to see "moral authority" given to the squelching of issues regarding minority rights and behavior.