Turning off replication will not effect the local movement of the HMD normally no, it sounds like your client somehow set it up so that the player is not fully possessing the pawn and is receiving camera replication on the camera they are using for their local view. The clients send their local camera transform out to the server via RPC and it is returned back to all (non owning) clients via a replicated variable.
Not entirely sure how that could happen, it would take some effort to break it as much as that. Its possible that they removed the Cond_SkipOwner part of the replicated variable?
I still have users in multiplayer in 4.22 so it is highly unlikely that a feature back port broke any of that (still possible, just very unlikely).
The camera updates its local position on GetCameraView, which should set later in the frame than replication, so the mostly likely outcome is some sort of setup where they aren’t fully controlling their pawn somehow.