I ask because I hypothesize that a rational theist/religious person almost definitely has to be vulnerable to Pascal's Mugging.

I don't see why they'd be any more vulnerable then a rationalist atheist.

Keep in mind we don't even know how to describe a rational agent that's not vulnerable to Pascal's mugging.

The way we currently get around this problem is by having a rule that temporarily suspends our decision theory when we pattern match the situation to resemble Pascal's mugging.