I would say that belief alters our perception of reality and our interpretation of reality, but it doesn't alter reality (individual or otherwise) at all.

> If you don’t believe in any God, your reality will be based on logic.

Hmm. This is an odd statement. I believe in God, and I believe in logic. You make it sound like anyone who believes in God checks their brain at the door.

> when a believer sees things such as a rainbow...

Hmm. When I see a rainbow, I think it's raining somewhere when the sun is shining through it. I don't take rainbows as signs.

If you believe in any God, your reality alters in a way that you feel it’s presence. If you don’t believe in any God, your reality will be based on logic.

For example, when a believer sees things such as a rainbow, they might take it as a sign, in which they feel the immense presence of a God. Non believers in the other hand, tried to understand the logic behind it.

What is true here is faith. Regardless of having or not having does not change the fact both parties can experience a rainbow but what’s different is how they let it effect their thoughts.