Bananas should actually make your stools softer and help keep your bowels moving instead of binding up your bowels.
However bananas that are not fully ripe can sometimes bind you up so it's best to wait until the bananas are fully ripe before eating them.
Non ripe or green bananas have a lot of starch, which can be hard for the body to digest which causes your stools to get hard and lead to constipation.
But ripe bananas should not cause any constipation.