Making sin illegal is just importing the set of rules from a religion into your existing law. If you believe these rules are the direct word from an infallible deity then it calls into question the need for mortal laws at all. If however you think that sins are idiosyncratic to each religion and often even to sects within a religion then you have to allow for the fact that they may have been created by fallible mortal means. If you allow for this, then you have just imported a mortal law in an effort to improve your mortal law. Even worse, religions can have sins like "you are not allowed to worship any other religion", which directly contradicts your existing law and would be extremely divisive regardless.
Imagine if the government made sin illegal, but chose Buddhism for the list of sins? Would you feel ok with this? Or maybe Shinto? How about Satanism? Or even if they did choose Christianity, but settled on Seventh Day Adventists? Separation of church and state is essential for a stable and diverse democracy.