Your website has exactly the same problem as mine. I setup a user Magmatest on your website:

went to profile settings
changed language to english
clicked 'edit avatar'
uploaded image 1
refreshed the page
clicked 'edit avatar'
clicked delete avatar in pop up box
chose image 2
clicked save
page refreshed with image 1
clicked 'edit avatar'
pop up box shows image 2

Ok I just did exactly the same procedure on this mylittle forum which is running 2.3.5 and the problem does not exist, the avatar changes no problem like it did before 2.3.7

I think that kind of proves it