Some 3 year olds are or can be embarrassed about wearing diapers and some 3 year olds don't mind wearing diapers or being seeing in diapers.
My own 3 year old son is embarrassed to be seen in diapers but he doesn't want to use the potty.
I keep telling him that if he uses the potty then he won't have to wear diapers anymore.
However I've known some 3 year olds that don't mind being seen in diapers and would run around in just diapers without any care.
I even have a neighbor who has a 5 year old boy who is not potty trained and he runs around in his yard in just his diaper or diaper and shirt in the summer and doesn't care what others say about him.
He's not autistic or anything but just refuses to use the toilet.
A 3 year old should not have his diaper changed in public when it can be avoided.
At 3 they are becoming embarrassed and self aware of their body and need privacy.
So it's best to take the 3 year old boy or even 3 year old girl into the bathroom or somewhere private to change their diaper.
If you have to change the 3 year olds diaper in public try giving them privacy by covering them with a towel, blanket etc.
A 3 year old can get embarrassed when having his diaper changed.
I have a 3 year old boy who is not potty trained yet and he's in diapers full time.
I used to change his diaper in public and wherever it needed to be changed.
However a few days ago we were at Walmart and I took him into the bathroom with me to change his diaper.
I lifted him up onto the changing table and started to remove his pants to change his diaper.
He screamed out and said NO MOMMY please don't.
I could tell he was embarrassed and so I took him into a stall and did a standing diaper change instead.
So yes 3 year olds can get embarrassed about having their diapers changed in front of others.
At 3 you should take them into somewhere private such as your vehicle, toilet stall etc to change their diaper.
At home take them into the bathroom or a bedroom and give them privacy while changing their diaper.
If the 3 year old is embarrassed don't embarrass them when they don't want to do something that you can give them privacy for.
At 3 they are becoming aware of their body and giving them privacy is a good thing.