I'm also not a religious person but I once had a very odd feeling after a guided meditation (I completely lost ALL fear of death for a couple days... including the baseline fear of death, which we all actually have and which I had never noticed before, since it's always there). It is good to be skeptical, but I think it's also good to acknowledge when something truly subjectively weird occurs.
That is a strong claim.
I have no fear of death, but a fear of what often immediately precedes death, namely decrepitude and illness. I'm in my mid 50s and so I watched the generation of my grandparents go through it, and then my parents generation. The only positive I can find in that is that if any of them feared death, the illness had made them prefer it over the constant sickness.
I remember one Hindu guy telling me after a long discussion in the sauna, "Ego is your brain trying to protect you from truths you cannot handle".
It left a lasting impression on me.
FWIW the guided meditation that got me to my "experience" was apparently inspired by Babaji