First off, there is a difference between membership in the NSDAP, the official and sole political party of the Third Reich, and the German armed forces, the Wehrmacht. Membership in the former was not mandatory but voluntary, albeit a number of Germans did join the NSDAP for non-ideological reasons such as to advance one's own professional career. But the Third Reich's military was a conscription-based force with mandatory levies based upon age cohorts. The dictatorship enacted only the most minimal provisions for conscientious objection although racial enemies, certain criminal convicts, and others labeled "asocial" were exempt from military service. So while membership within the NSDAP was not compulsory within the Third Reich, Aryan Germans of military age typically had little choice but to serve.
The party existed in an anomalous position within the German military. The Wehrmacht initially held the position that it was an apolitical institution and in the thirties all NSDAP members had to resign from the party as a precondition of service. This restriction was waived or ignored as the military expanded and rendered the apolitical nature of the Wehrmacht fictive. There were multiple examples of NSDAP members serving within the armed forces during the war.
There are a number of factors that make it difficult to give a firm projection of the numbers. Destruction of documentation of membership and other personal files during the war certainly has made this process difficult. The regional nature of German recruitment where individual units from the same geographic area (Wehrkreis) makes it difficult to extrapolate a general picture as NSDAP membership could vary widely from region. NSDAP membership also fluctuated somewhat during the war because the crisis in German manpower forced the Wehrmacht to draw from younger cohorts. Accelerated officer training programs of younger troops, many of whom came of age after 1933 and were thus more socialized to National Socialism. Studies of extant cadet school members mid- and late- war show that many of them held leadership positions within the Hitler Youth and SA. The various branches of of the Wehrmacht also quite different and attracted individuals from different parts of society and had different age cohorts. Hitler reportedly quipped that he possessed a reactionary army, a monarchist navy, and a National Socialist Luftwaffe.
In general though, the officer corps' NSDAP membership hovered at around 30%. This is not surprising given that the officer corps recruited largely from the middle class and this was a sector of society which the Third Reich had made a great deal of inroads in recruitment. An important aspect of an officer's career were also officer assessments for "National Socialist convictions" in which a qualifying officer would judge the officer's commitment to the state's ideology.
Apart from membership within the party, there were other avenues of NSDAP socialization that influenced officers, and, by extension, the Wehrmacht as a whole. When the war turned against Germany, the military instituted Nationalsozialistischer Führungsoffizier (NSFO) to inculcate ideological mentality among the troops. The various organizations like the Nationalsozialistisches Kraftfahrkorps (NSKK) and Nationalsozialistisches Fliegerkorps (NSFK) (N.S. Motor and Flying Corps, respectively) were popular youth paramilitary organizations in the 1930s. These groups had a strong ideological component to them in addition to providing German youth opportunities to indulge in operating modern machinery like cars and gliders. The Reichsarbeitsdienst (RAD) was a compulsory youth labor service that grew out of Weimar organizations and aside from building bunkers, the RAD had a strong component of ideologically charged socialization; RAD members were to be Aryan and there was a pedagogical component to the RAD to prepare German youth for military service. This meant that a large percentage of German youth had gone through some level of National Socialist organization, some voluntary, others compulsory by the outbreak of the war. This is apparent in the NCO's level of commitment to the regime and the NSDAP leadership style. Despite being of different social background than the officers, NCOs typically had a similiar degree of commitment to the regime. These multiple levels of socialization and indoctrination helped forge an ideological component to the Wehrmacht that the postwar myth of the clean Wehrmacht tried to erase.
Sources
Bartov, Omer. Hitler's Army: Soldiers, Nazis, and War in the Third Reich. New York: Oxford University Press, 1991.
_."Soldiers, Nazis, and War in the Third Reich." The Journal of Modern History (1991): 44-60.
Militärgeschichtliches Forschungsamt. Germany and the Second World War, Volume V/II: Organization and Mobilization in the German Sphere of Power, Wartime Administration, Economy, and Manpower Resources 1942-1944/5 Oxford: Clarendon Press, 1990.
_.Germany and the Second World War, Volume IX/I Politicization, Disintegration, and the Struggle for Survival. Oxford: Clarendon Press, 1990.