It is okay for your 3 year old son to wear just his diaper outside if it's warm enough or hot out.
Nothing is wrong with a baby or toddler running around outside or in the house or even in public wearing just their diapers and shirt or just the diaper.
You're not a bad parent if you allow your kids to run around the house or even outside with just a shirt and diaper on.
If it's in your house then it's nobody else's business if you allow your kids to wear just a diaper and shirt in your house or your yard.
Kids love to be in just their diapers and it's easier to keeping them clean as well.
Having your kids in just a diaper and shirt means less laundry, makes the kid more comfortable and it also makes it easier to check and change a kids diaper when they are not wearing any pants or clothes over their diaper.
I also don't see a problem with kids and toddlers and babies wearing just a diaper and shirt or just a diaper outside in public.
During the summer my kids would be out in just a diaper and I've even saw a kid around 6 years old at a park this summer wearing just his diaper, shirt and shoes and it did not bother me.
I think he had autism and needed to wear diapers and having him in just his diaper kept him cool and comfortable.
I've had a few weird glares and some comments from judgy people about my kids being in just their diapers but I don't let it bother me.
I take care of my kids the way I want too and if they are comfortable wearing just a diaper or just a diaper and shirt then that is how they should dress.