Agreeing that one should assign some uncertainty to claims doesn't mean one is necessarily a Bayesian. Additionally, while this may get into a definitional disagreement over what it means to be a Bayesian, agreeing not to use 0 and 1 as probabilities for real world events is not generally considered to be a fundamental of Bayesianism.
I would edit your second statement to say is not generally considered to be exclusive to Bayesians. But both are correct.
http://bigthink.com/think-tank/neil-degrasse-tyson-atheist-or-agnostic
Apparently Dawkins and Tyson give a non-zero probability to "God". Which is pretty much what is expected of a rational person. And of course it will be used by theists to say "They aren't really sure!"