Morality arises immediately from the fact that we are social beings and that this social dimension to our lives is not subject to our choice; we cannot choose not to be social animals any more than we can choose, say, not to be vertebrates. The constraints and compulsions that our social being imposes collectively upon us (although, of course, individually we can choose to disregard those compulsions and constraints and perhaps get away with it) are not matters of collective choice. A society that chooses to deny, for example, the moral primacy of truth over falsehood must collapse - unless it rediscovers honesty in time.
We are social beings and the moral consequences of this fact cannot be gainsaid. It is open to anyone to believe that this is so because God made it so; it is open to anybody to find the god hypothesis to be unnecessary and therefore to apply Occam's Razor to it. 'God' is a possible explanation of morality but our need to be moral does not hinge upon that explanation being objectively true. Liberal Democrats and others are none the worse for being secular humanists.