Harold and Susan Vordos wrote:
....
If your die is adjustable, open it up so you take two passes, one to rough
the thread, one to take it to size. Cut or grind a chamfer on the end of
your material, and make sure it's uniform, so it assists in starting the
die, not only square, but concentric with the material.
....

A few times I've left some extra length, turned to root diameter,
to start a die out straight, and conversely when tapping, drilled
a little ways at ridge-diameter size to start a tap straight.
Home shop expedients ...

Don't permit the die to start crooked with the idea you'll get it to run
straight once started. That works about as well as a pig on stilts.
....

I've never seen a pig on stilts so couldn't say.
Your varied experience never ceases to amaze me!

-jiw