You also notice your language when discussing this? That people who work in Starfleet are rational, scientifically-minded people? And that anyone not of that mind-set is inherently too flawed to fit into Starfleet?
In a sense. They must be able accept the scientific reality (this does not necessarily mean they have to be an atheist.)
I cannot imagine a person with a level of disconnect from reality and mistrust of science exhibited by creationists and climate chance deniers working in the Starfleet.