Had the same issue using an AMD Graphics Card on Windows 10 here.
Reinstall didn't work. But the following did
AMD Settings
Create a profile for Minecraft Launcher
Set Shader Cache to "On" instead of "AMD Optimized"
The Skins Tab is now working for me. Hope this helps.
Abrar Ahmed
Had the same issue using an AMD Graphics Card on Windows 10 here.
Reinstall didn't work. But the following did
AMD Settings
Create a profile for Minecraft Launcher
Set Shader Cache to "On" instead of "AMD Optimized"
The Skins Tab is now working for me. Hope this helps.