I am also having this issue. I play on an iPad Mini 4. When I tried using a new skin it refused to display it and kept it as the skin I already had. I restarted Minecraft and it now crashes each time I try to go to the change skin interface. If it helps, I renamed my skin from a png to jpeg, but later converted it again through GIMP because the file was not actually registered as a jpeg and had remained as a png. Maybe that's why it's crashing?
I can confirm I am experiencing the same issue on 1.13.0 for iOS.