The rallying cry that only secular laws should govern men, and that only secular reasons should be behind those laws, is complicated by there being no secular reasons to begin with.
Or rather, if there are secular reasons - if ultimately a secular reason is just any reason that is not rooted in the commands of a deity or of a "religion" (whatever that is anymore) - then the rule is useless, because it's trivial to take any given reason that is normally rooted in God's existence, God's commands, or the commands of a religion, lop off the parts that are invalid, and simply substitute 'that's just what I like' or 'that's what I value' in its place. All of your religious views about what is right and wrong can become 'secular' in a heartbeat - and without sacrificing an iota of your religious beliefs, no less.
This is short, simple, and straightforward - and also, I'm convinced, inescapable. But I think it's an idea that has yet to sink into the awareness of the religious populace at large, at least in the West. At least part of this is probably rooted in the old idea of Athens versus Jerusalem - that there is faith over here, and reason over there, and while they may run parallel at times, they are not the same thing, and at least in some fundamental sense they are at war with each other. If you have 'faith', whatever that is, then you are in Jerusalem - not Athens.
I've never been on board with that idea, but recently I've come to reject it entirely. It's a false contrast.