This is a random bug that has been occurring recently for no given reason. I’m not sure why it is caused but I checked to see if I did something wrong and I can’t seem to find the issue behind it, so I assume its a Engine Bug. Animations that I play on my client doesn’t play on other people’s clients randomly, it does it whenever it wants to. I’ve checked to see if the NetworkOwnership was an issue and that doesn’t seem to be the case. Any explanations?
When it wants to replicate:
When it doesn’t want to replicate:
The NetworkOwnership being fine: 
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reprofile.rbxl (119.4 KB)
Make sure you run a 2 player server so you can watch both screens and see how it doesn’t replicate.
You need to activate flight mode, and to do that you double press space.
Once your in flight mode:
W,S,A,D - Move around
Space - Ascend(Go Up)
C - Descend(Go Down/you will land if you touch the baseplate.)
As you watch the other person’s screen or the server’s screen. The person that’s flying’s animations won’t replicate except on their own screen. Thank you.