Not exactly. Shoes make the situation worse, but don’t actually cause the stinky feet problem.
Feet stink because they produce a lot of sweat which is eaten by the bacteria that thrive naturally on everyone’s feet. Lots of bacteria feeding on lots of sweat excrete lots of waste and it’s the waste that’s stinky.
Even bare feet can get sweaty and grow a bumper crop of bacteria which can result in stinky summer feet.
Because so many people wear sandals or even flip-flops in the summer, there is no hiding from those stinky feet. Everyone around you will be able to pinpoint the source of the offensive odor.
Don't let this embarrassing moment happen to you.