For anyone else who comes across this:
I had the exact same issue as Integralo described in the OP. Turns out the fix was MUCH simpler than the major replication problems I was suspecting.
This old forum thread contains the solution: multiplayer, 3rd person and terrible stuttering.
tl;dr: make sure “Orient Rotation to Movement” is turned off in the CharacterMovement settings if you converted the 3rd person template to first person.