What often happens is that people have "mystical" experiences and then make all sorts of assumptions which aren't warranted.
Agreed.
Theists may pursue the mystical experiences, but then they make a mess of things by trying to pile of bunch of explanations on top. That is, they don't value the mystical experience for itself,
they lack sufficient faith in the experience, and so they think the experience requires embellishment and improvement in the form of explanations, which they grab from pretty much anywhere they wish.
Atheists may be so very intent on discarding the explanations that in their panic to do so they confuse the explanations with the mystical experience, and thus toss the mystical baby out with the explanation bath water.
In both cases, both parties have chosen a recipe book over a nourishing plate of food, and then they wonder why they're still hungry.
A way to bring this epic pointless debate to a conclusion is remarkably simple. Discard all the explanations
and anti-explanations. Just let them go. In the toilet bowl they are placed, flushing the handle now, watching them go round and round, and then they're gone. Bye bye!
Once the explanations and anti-explanations are gone, there's nothing left to do but pursue the experience, or not, as one prefers.
Some will move on to other topics where credible answers can be found. Others will want to continue with this ancient inquiry. Both of these are reasonable choices each of us are entitled to.
For those who wish to continue the inquiry, the only serious question is....
How do I have the experience?
This is not esoteric. It's no more complicated than the hungry guy who asks, "Where do I get a meal?" If we see a homeless person on the street asking for food, we know they are serious, and merit our response. If they are asking for money for a fancy cookbook, we know they aren't serious, so we tell them to get lost. Like that.
Once the explanations and anti-explanations are gone, the experience is no longer a religious experience or an atheist experience, but a human experience. Like eating food, or taking a nap, or having sex. We have a human need, so we meet that need. Simple. Nothing here to argue about.