A big difference defined by one little word, evidence.

Well to begin with your premise is wrong. An agnostic is simply one who doesn't know whether God exists or not. That has nothing to do with the soul. An atheist simply doesn't believe in God. Again nothing to do with the soul. There are atheists and agnostics who believe in spirits and souls and even an after life. They simply neither know or believe God exists. Many cultures have had beliefs in such things without gods. I.e. several native American tribes believe in spirits, respect them and yet do not deiefy them. Saying atheists and agnostics deny the existence of a soul is patently false. They make no such claim.

As to the religious, depending on the religion or subset of a religion they do not deny the flesh. In Christianity the bible says to take care of your body. It gives instructions on how to keep it healthy and clean. Not the best instructions but they are there and many Christian's take it to heart, treating their body like a temple.

Now physical well-being may not actually be what you meant however the question I would say was poorly worded and not specific enough. If you made it more clear what you meant then I can answer that too, to the best of my abilities.

Without benefit of a scientific perspective, the ancients didn’t have the same understanding we do of the concept of ‘mind’ and particularly of ‘subconscious mind’. But they could observe that SOMEthing was animating the body. They called it ‘soul’. We now call it ‘mind’ and claim there’s no such thing as ‘soul’. It’s not a reality problem; it’s just a linguistics problem. Every time you hear the word ‘soul’, just replace it with the word ‘mind’. No extra belief required. I’m not aware of anyone who doesn’t believe in mind.

It sounds like you are not willing to bet against Pascal's wager. I'm betting my life that he does not exist. According to the bible, sitting on the fence does not count. Either your in or you out.

Pascal's Wager is an argument in philosophy presented by the seventeenth-century French philosopher, mathematician and physicist Blaise Pascal. It posits that humans bet with their lives that God either exists or does not

The body exists. The soul is a word people used back in the olden days to try their best to explain consciousness, feelings, love etc. it doesn't exist as a separate thing.