Voting does not make it right, case in point the POTUS.
I believe it is, and the authority is derived from the preamble to the Constitution, "We the People," which is the final authority for all matters on this earth.
If the people deem a burka is a threat to their security, they have every right to ban it. If the people decide Islam is not a religion compatible with the Constitution, they have every right to abolish its practice, or take any other action to mitigate its influence.
But I'm not talking about a government operating outside of its restrictions; that may be the distinction: the people have no such restriction.