I don't know if I can speak of a religious experience, because I don't consider myself religious. I'm a pretty firm believer in the law of thermodynamics but that's about it. I've often joked that the donation was me jumping the gun on my atoms being recycled into something else.
Maybe because of my lack of belief in a higher power or life after death, there was a time when I struggled quite heavily with depression and the sense that nothing mattered, that the world would be better off without me and the usual self-depreciating spiral of negative thought that can happen. It got bad enough for me to seriously contemplate suicide. Thankfully I got wonderful help and I think I got out of it knowing a lot more about myself.
And in a way, even though the depression happened more than 10 years ago, giving a kidney gave a certain meaning to my life. I didn't set out for it to be something as life changing as it turned out to be. It's just something I felt compelled to do. If I could then I -had- to do it, often struggling to explain rationally the drive I felt to donate.
And now, all those old thoughts that my life didn't matter, didn't have an impact, were all measurably proven wrong. To someone somewhere, it mattered, big time. I won't purport to have found the meaning of life, but seeing how life affirming donation felt, it helped me understand that meaning and happiness, doesn't magically happen or isn't found in a bank account, it's not even inside you. It's inside others and how we make them happier.
Maybe it's sort of post-donation high that will subside over time but I've found that I'm far happier post donation. It's like a weird little invisible badge of bad-assness that my self-esteem can hang on to when the going gets rough. It's the one accomplishment that nobody or nothing, not even depression, can ever take away from me.
So, religious experience? I don't know. But definitely life changing.