When I try to change the personal photo of anyone in my tree, the window that comes up sits and spins for at least 1 min often up to 2 or 3 before showing the thumbnails that can be changed to.
I have checked your family site and I see that you have many photos in your site (thousands...).
When you try to change the personal photo, it retrieves all photos of that person from the server and that can be longer if there are many photos associated to that person.
I would understand if it were many for an individual. However this happens if there are 2 photos for a person or 20. I double checked and my grandson (in the attached photo on the OP) is only tagged in 7 photos.
One thing I have found is that if you let it 'sit and spin' for a minute or two and then cancel, often it will come right up. Not always but a lot. Sometimes that just results in waiting again.
So it seems like it is going through all photos for the site rather than just that individuals - at least at first. Or it is building some kind of cache and gets hung up and then when you cancel and restart the process it is done.
Am I the only one seeing this? Or perhaps the only one reporting it...