Otherwise, who knows what could happen?

The opponents--the right wing "Christians"--can't handle thinking for themselves. It's too scary.
If other people aren't required to follow their rules, well, then the possibility exists
that they don't have to follow "the rules", either. The problem is, their "rules" are based
on arguments from another time and place (2000 years ago)which are meaningless in a society
that has evolved to value "liberty and justice for all".

On edit: it's the same reason so many of them fight the concept of evolution: it implies change.
They can't handle change.