I'm having exactly the same problem with a brand new iPhone XS. My previous iPhone X didn't exhibit this problem.
I have 16 entries on my "Favorites" list. I added and changed the order to notice that iOS 12 keeps changing it, even when I'm fixing it. Line and spacing bugs (entries become vertically longer) are also present.
So far I have managed to "handle" this bug by making one change at the time (Edit-change-Done) and moving items withing the visual range (if the list scrolls, then it does not work).
This is terrible, as I change the order with some frequency (due to international travel) as there are different numbers for the same people. I keep the "current" number on top and save the others on the bottom, and eventually I revert. With this bug, this becomes a major pain.
I hope Apple fix it soon.