Michael Koblic writes:

How does everyone manage to get a straight thread when die cutting?

Chuck work in lathe. Position die in holder by hand at the end of the
work. Push up against opposite side of die with tip of closed drill chuck
in the tailstock, so it keeps the die "normal" to the work. Turn die
handles back and forth by hand while feeding tailstock.

This holds the die in two angular degrees of freedom, "pitch" and "yaw", if
you will, and in the Z axis. Does not constrain the "roll" (which you want
to spin by hand anyway), nor the X and Y, which are roughly constrained by
the self-centering tendency of the die around the work.

Reality is always 6 degrees of freedom that must submit to your will via
tools.