No. But people act on their beliefs. Beliefs determine morality.
And "without God, everything is permissible."
You omitted my qualifier, which said no one should have a problem with another person's belief "as long as it doesnt break your leg or pick your pocket."
I was a libertarian in my '20s. It's not the worst philosophy in the world, but it's very shallow, and rests on nothing.
If you want truth and depth, try Aristotle and Aquinas.
The important thing is that beliefs do not determine reality. Morality is a way for mankind to deal with reality.
And "without God, everything is permissible."
A silly assumption. On the contrary, everything is permissible if you believe God is on your side.