If Field Marshall Erwin Rommel did not support the Nazis or Hitler, why did he fight so long and so effectively on he battlefield to defend their...

I would agree with the above answer, and this was true for
many Germans during the war who were never supporters of the Nazis, but were in the war
to defend the Fatherland, for better or for worse.

Rommel
is a very interesting character, and the essence of the honorable Prussian officer.  He
treated all prisoners humanely, even Jewish ones, ignoring orders he had been given to
kill them upon capture.  The Afrika Corps he commanded in North Africa and gained fame
for leading as "The Desert Fox" was never accused of war crimes during the fighting
there.

Rommel fought so well because he thought it his
duty, and because he loved his country.  He wanted to exemplify what he thought a German
officer should be (as opposed to the example of the Waffen-SS), and later, in 1944
during the bomb plot against Hitler, he wanted to, in his words, rescue
Germany.

There were others like him.  Karl Doenitz,
commander of the Germany Navy and last leader of the Third Reich, and Wilhelm Canaris,
head of the German Abwehr, or spy agency were either passively or actively against
Hitler while continuing to serve and defend their country.