Changing a diaper should be private as it's just the decent thing to do.
The baby will not be embarrassed by getting their diaper changed if it's not private and around people even if they don't know them.
However I personally have always gave my babies and toddlers privacy when changing their diaper and would always take them away from others even family to change the diaper.
When at someone else's house I would take the baby or toddler to the bathroom if possible and change the diaper there or take them out to the car.
I would not allow anyone else around the baby when I changed their diaper.
The diaper covers private parts which are called private for a reason and nobody needs to make a show of a diaper change or even video it or take pictures for that matter.
My sister wanted to take pictures of me changing my kids diapers when they were little and I would not allow it.
She said that I was being unreasonable and that they were just a baby or little one and it would not matter.
But to me it would matter.
You don't have to change a diaper in private but to me it's the decent thing to do.
I also don't like it when someone changes their baby around me even if it's a relative.
But if you need to change the diaper then try to cover them up to keep their genitals out of view and get the diaper change done as quickly as possible.
If it's a 2 year old, 3 year old, 4 year old etc that is getting a diaper change then in those cases the diaper change should be in private.
I've seen some 3 year olds get embarrassed looks on their face when their parents changed their diapers right out in front of people.