It’s likely because of network ownership issues. It will bounce between both the server and client, which will cause it to stutter.
Add this line into your code, right after the variables:
character.HumanoidRootPart:SetNetworkOwner(nil)
Setting it to nil with the HumanoidRootPart will prevent it from bouncing between the two, which should prevent the stuttering.
You already do this with every single part, but that is not necessary. I would try just the HumanoidRootPart
Also, I would recommend to just changing this to a repeat loop:
repeat task.wait(1) until game:IsLoaded()