Yes when at home it's okay to let toddlers run around at home in a diaper with no clothes.
At home toddlers and anyone else can run around at home in underwear, diapers and even naked.
When I was a toddler I would run around our yard and inside the house wearing nothing but a diaper or sometimes a diaper and shirt and shoes.
Outside I had on shoes with my diaper and loved running around that way when it was hot.
In public though my mom always put shorts or pants over my diaper and she never let me go outside in public places wearing just a diaper.
I have no problem though if a kid or toddler or baby is out in public wearing just a diaper and shoes but really it's best to have the toddler or child wear some shorts and a baby should wear at least a Onesie over the diaper.
At home it's perfectly fine for a toddler to run around in just diapers but in public they really need clothes.
People tolerate toddlers and kids in just diapers in public but in reality it's not socially acceptable for toddlers and children or even babies to wear just a diaper while in public.
Also it's not socially acceptable to change your babies or toddlers diaper in public either and especially not at a table where people are eating.
Take the child or baby into a bathroom or into your car when possible to change their diaper.