I have the texture packs turned on under global resources when this happens. This occurs on my iPad Mini 4th Gen and my iPhone SE 1st Gen. I haven't checked if the Windows 10 version does the sane yet.
Only Allow Trusted Skins has nothing to do with it. We can see our own skins. This is related to a previous bug where we would get each other’s skins in multiplayer games.
UPDATE:
I have since opened Minecraft on all of my devices and joined the same world on all of them. I then turned OFF Only Allow/Show Trusted Skins on all of my devices, this caused the selected skins to show again.
For some reason, this is not on my account anymore so I can't edit it. I have a bug report that is the same at this, it is MCPE-126012