There are five skin slots and if you select any slot that isn’t second (from left to right) the game might equip the second slot on its own occasionally. Usually it doesn’t happen, but sometimes, when you open the game, the second slot will be equipped instead of whatever you had selected before.
MCPE-229249
An equipped skin keeps changing
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1
I am having this issue as well except it's not the second slot for me, but rather steve or another character instead of my equipped skin. The only thing I found that helps is before going to any realm or world, switching and selecting my skin again right before.