I can only speak about the rules around our communal pool which we share with mostly our Turkish neighbours; they treat shoes around the pool platform in exactly the same manner as wearing shoes to enter their homes, the non slip argument is not even a consideration, by the way, the skin on the underside of your feet has superior anti slip properties than flip flops. The T-shirt argument is a bit more complicated, firstly our Turkish residents consider that clothes will dirty the pool, I have heard stories about Turkish Ladies who have felt the need to swim in more than a costume, they wash the swim clotting in running water before putting it on to enter the pool.
The other factor is that any material holds traces of enzymes from the soap powder they were washed in, these enzymes neutralise the expensive pool chemicals which sometimes leads to a complete water change being required. To do this is mega expensive.
Rimms