Although it might not be illegal in your town or state you will likely get stopped and questioned by a cop.
Then he/she could find some other charge to arrest you with.
You could also be made the laughing stock of the town if you go about wearing just a diaper in public.
Cameras are everywhere now with tablets, phones, etc and you're picture or video will likely end up on youtube or national television.
Don't do it. If you want to run around in just diapers do it in your own home, or in your own yard if it's fenced in.
A lot of people including me don't think it's cute when a baby goes out in just a diaper. They should be clothed too and shame on the parents for letting them out in just a diaper.
It's not decent for them to be out in just a diaper and it's not the decent thing for you to do either.
Keep your clothes on in public.
Diapers aren't just like regular underwear. Diapers are used for holding urine and poo and no one wants to see a urinated in or pooped in diaper.
It grosses me out when I see a baby or toddler in a wet or poopy diaper it would really gross me out to see an adult or older person in one.