When playing with another player on a world hosted by either of us broadcasted over LAN, one of our skins will take on the appearance of the others. this is true for both players, although each player sees that the other player still has his/her original skin. This bug tends to be unpredictable, especially in worlds with more than two players.
Thank you for your report!
We're actually already tracking this issue at MCPE-48207, so I will resolve and link this ticket as a duplicate.
If you would like to add a vote and any extra information to the main ticket it would be appreciated.
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