A genuinely democratic society requires a secular ethos: one that does not equate morality with religion, stigmatize atheists, defer to religious interests and aims over others or make religious belief an informal qualification for public office.
For democrats, it's as crucial to defend secular culture as to preserve secular law. And in fact the two projects are inseparable: When religion defines morality, the wall between church and state comes to be seen as immoral.
If believers feel that their faith is trivialized and their true selves compromised by a society that will not give religious imperatives special weight, their problem is not that secularists are antidemocratic but that democracy is antiabsolutist.