The notion that one is a Boltzmann brain doesn't really change anything. If you are, there's absolutely nothing you can do about it. So the only sensible thing is to assume that you aren't, regardless of probabilities.
I must say, with Trump, Brexit, war, and more Trump: Well done, folks!
Also, there is at least a connection to experimental physics in that we can measure "virtual" particles (e.g. Casimir effect) and can calculate their probabilities etc. There's no such underlying experiment for God(s) that I'm aware of.
God itself can be supernatural, but feels like it can only affect a limited part of any universe due to the limitations in observer’s mind. If we could expand BB size indefinitely up to the size where it stays coherent (light milliseconds?) then that would basically cover everything that a consciousness itself could experience. This makes God infiniteness sort of redundant and unclear why it would be needed to generate a universe.
This echoes with my vague idea that hypothetical FGH-sized beings are indistinguishable from God(s) whose infinite part could actually create more issues than it might solve.
Iow, we have to define some Continuum of reality for God of omega+ size to operate on, not to mention Proper Class sized God. Our ancestors really overkilled this idea, but little did they know. So maybe we should take its infiniteness as “anything imaginable by an arbitrarily-sized BB” rather than its naive infinite meaning.
The reason I don't agree with the parent comment is because to truly believe in a Boltzmann brain would seem maximally nihilistic.
Many people truly believe in God/gods at their deepest level. While the Boltzmann brain is an interesting thought experiment, I don't think anyone really takes it to heart the same way a Christian believes in Jesus.
Even while I would probably give the Boltzman brain a far greater probability than most, people don't go around telling other people this is all just a momentary, random fluctuation.