I have been working for UPS for about 21 months now, and I have worn regular tennis shoes since day one. Oddly enough, I've never had a single comment on them. I wear shorts year round, and they are distinctly tennis shoes, no mistaking them.
However, when anyone in my area, or anyone I've seen wears anything but boots, they get sent home.
I've only had one injury since working there, and it had nothing to do with my shoes. I've had my sort manager see my shoes and had nothing said. I work in the unload, where obviously it COULD pose a problem, but I've never injured my feet or toes. Call me stupid, but I prefer to wear tennis shoes. The one or two times I've worn boots I found my feet feeling unprotected. My tennis shoes are the only way I will work.
I am not really sure what I am trying to say with this post, but if your supervisor says something about it, then do it. You are there to listen to your supervisor, not make your own rules. If my supervisor told me to get boots I would do it right away. If I get sent home it's my OWN fault and I know it. I am not going to point out that other people aren't wearing boots. Maybe they've been talked to in private, or maybe you're just not well liked. Whatever it is, don't push it off as "Well he can do it so why can't I?"