There is an enormous difference between a) having your morality at least informed by religion, and b) having religion directly influence law-making.
Part of the problem is that a lot of the philosophical principle, if you will, in the Bible is not unique to the Bible. The so-called golden rule (treat others as you would be treated), for example, has a strong relationship to one of Kant's imperatives (act as though the maxim of your action was universalized).
Second, there are a lot of people who believe that some portion of the law, particularly the Constitution or other framer-ideals, come from the Bible when in reality they come from some other source. Its just that the ideal is common to both the Bible and these other sources and so people assume that it was religion-inspired when it may not have been.
Certainly Christians recognize that it is possible to be good or to do good things for or by people that are non-believers. So, its not that the Bible has a lock on all things moral or good.
On the other hand, just because a principle is found in the Bible does not mean that implementing the principle, at least in the big sense, is enforcing religion on the rest of society. The fact that the Bible instructs not to kill, for example, does not mean that all laws against murder in this country are based in religion.