what if you pulled somebodies outie belly button out?

Their ass would fall off.

You would get blood on your pliers!

or what if you pushed it back in?

If you push it in, it will pop back out, just like when you post the end of a balloon into itself.

You'd probably get a five finger sammich. ʕ´•ᴥ•`ʔ

Mikers do you think it would stay!

You would get a poke in the eye.