This isn't hard.
Many of the top RPGs for any of the systems listed fall within your parameters.
For PS1....
Star Ocean The Second Story has some religious references in some of the names of things, but otherwise falls into your parameters.
Wild Arms / Wild Arms 2 have some similarities to Native American religion/heritage, but that's about it
Chrono Cross...great game. No religious themes I can think of.
Vagrant Story
You probably want to avoid....
Any Shin Megami Tensei game (including the Persona series)
Xenogears
Legend of Dragoon
Grandia II
One thing to also look at is that the Japanese culture often incorporates religion into their stories. So JRPGs will often have references, if not a direct tie, to some form of religion. If a game looks interesting, a quick google search can help you to stay away if its contents are offensive. What happens a lot is that the "church" becomes the villain. Not to say the Catholic Church, but often it is derived from a monotheistic religion with angels/demons, etc. Another popular trend is to take legends or creatures from a religion and encorporate them into the game. Not even necessarily from the religion itself, but rather from something like Paradise Lost or mythology. Beelzebub, Cerberus, harpies, and Death are all very popular enemies in games. So you are bound to come across a few, especially in JRPGs.