Haha thank you for playing. The clothing items are supposedly stand-ins for upgrades that modify some player or pigeons stats.
I think it's currently kinda "hidden information". If you play the game on desktop you can hover the mouse over the items in the shop and after a few moments it will display a tooltip describing what each item does. You can't see on mobile yet. I think a lot of players kinda miss this info for the most part. We plan to update the game with some quality of life updates which will include a UI to make this info clearer to the players.
Thanks again for playing!