Threaded dies floating in threaded press holes will tilt when they float laterally. You're better off making sure the shell ram, shell holder and cartridge case can slide around a little to align with the die (i.e. some polishing and lubrication). Even more importantly, pause at intervals on the way up and down in the stroke, to take the pressure off and allow things to re-align. Or use a press such as the co-ax that does not shift alignment during the stroke like conventional presses do, and allows the die to float laterally without tilting.
Also, different types of lock rings affect initial alignment. It is virtually impossible to get a set-screw lock ring locked in place square on the die body. The set screw forces the lock ring off-center to the die body, which then forces a tilt as soon as the lock-ring & die are tightened in the press. In this regard, the Lee O-ring system is better, but the Forster/Hornady cross-bolt lock rings are better yet. They lock in place securely and squarely. The lee lock rings are too easy to move out of adjustment while swapping dies, and the compression of the o-ring makes it difficult to repeat the exact same depth of the die in the press.
Andy