Speaking of examples, imagine a football club that has signed a sponsorship contract with Adidas, and then one player goes out on the field wearing Nike football boots.
You are wrong and this is happening all the time, but you are clearly not watching football matches

Every player can choose any boots they likes most and make individual deal, club sponsorship is only for shirts and kits.
I will give you one example of Real Madrid vs Girona, club have Adidas kits sponsorship, and Rodrygo wears Nike Phantom GX SE.
Here is highlights of this match:
https://youtu.be/AcgDUg4jIh0And here is Rodrygo boots:
https://www.footballbootsdb.com/player/Rodrygo/77572/