When you try changing your skin in a world or even from the opening screen it remains the same until you leave the game. Me and my friends have been having this problem for a while, and we even have different types of phones (all iOS). This bug occurs with our own skins and with the skins that Minecraft provides. This has been a problem for a long time, but I was waiting until the new update to say something, and the bug was not fixed.
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[Mod] Celesian
migrated
Thank you for your report!
However, this issue has been closed as a Duplicate of MCPE-37926.
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