I recall no reference to shoes in the rulebook. I doubt that that concrete in the summer sun is any friend to bare feet, - mine get hot in tennis shoes - but I doubt anyone will try to stop you. Putting the gun on your toes is mentioned as a bad idea, again as I recall, but not prohibited in the general ATA rules, though it well may be in the youth program which has suffered some unfortunate and visually upsetting occurrences. If you had seen the pictures, I doubt you would place a loaded gun on you toes, shod or no. N1H1
I would hope that individual clubs would have rules that would cover common sense safety items such as this. Bet the clubs' insurance carriers would too.
Adults wear "flip flops" at many shoots I have been to, and some are pretty damn good shots. Not about shoes, but I have seen some guys in those T shirts that are slit down the sides with very little in front and back and most look like they have a "fur coat" on, LOL