for an observer at 30 degrees N latitude what is the max angle between
the observers southern horizon and the moon?

Since the Sun, Earth and Moon all lie in the same plane, the answer is
the same for the Sun or the Moon:  83.5 degrees.  The answer would be
90 degrees (straight overhead) at the Tropic of Cancer, which is
located at 23.5 degrees N.  The difference between your latitude of 30
degrees and the Tropic of Cancer is 6.5 degrees.  Taking 6.5 away from
90 gives 83.5.  The Sun reaches this elevation once per year (June 21)
and the moon reaches it about once per month.