Rommel commanded Hitler's military bodyguard during the occupations of Austria, the Sudetenland and the balance of Czechoslovakia, and during the Polish Campaign, as well as serving as the Army liaison officer with the Hitler Youth. You didn't get put in charge of keeping Shicklegruber alive if they had any doubt about you loyalty to National Socialism. That was one reason Rommel joining the conspiracy was such a shock -- he had been the guy in charge Hitler's Army Bodyguard. It is also probably a big reason he was allowed to commit suicide. Goebbels had built him up as a National Socialist General, and Rommel turning on Hitler could not be dismissed as the action of some reactionary monarchist, as Goebbels tried to do with the guys with "von" in front of their names.
You forget, there were some people whose lack of fidelity to Nacism were overlooked by Hitler because of his respect for their abilities. Take Ernst Junger for example. And how do you explain Canaris lasting as long as he did?
Rommel, like most military men, liked Hitler, feeling that AH would do very well by the Army and understood their needs. This, however, does not make one a Nazi.