By default, animations replicate to all players in the server, even if called from a LocalScript in a FilteringEnabled game, I propose a simple feature request to enable a bool parameter inside the :Play() method of the AnimationTrack object that will enable or disable the replication of that said animation to other players.
Animation:Play(true) would replicate, while Animation:Play(false) would not.
Currently we have Humanoid.DisableAnimationReplication however that disable all animations from replicated while you may only want to disable one or two animations from replicating to other clients.