No. Because Hitler didn't need them to.

The German military back in the day operated in a manner somewhat similar to the Egyptian or Pakistani military today: as a "deep state" that saw itself committed to the German nation regardless of government. Even Bismarck was not permitted to attend the Supreme War Council in his time. Military and political administration in the German Empire and in the Weimar Republic were staunchly separate - Christopher Clark, in Iron Kingdom, argues that this separation is what led had to the Herero and Namaqua genocides in German SW Africa: the civil administrator, von Leutwein, had intended to simply outfight the Herero and force them to make peace on German terms, however, unable to control the uprising with his own forces, he had to send for the Army. The military saw things differently, and Gen von Trotha instead decided to commit genocide. Because the civil and military administrations were totally separate, there was nothing anyone in the civil administration who might have wanted to stop the bloodshed could do until it was too late. In the Weimar Republic, during the Kapp Putsch, President Ebert asked Reichswehr commander von Seeckt "where does the Army stand?" "The Army," replied von Seeckt, "stands behind me".

Even during the beginnings of the Nazizeit, the Army was still able to exert some of its old independent authority: Hitler secured their loyalty with the "pact of the Deutschland", whereby he agreed to massively expand the Army and curb the Brownshirts, a process which culminated in the Night of the Long Knives. After von Hindenburg dies, the Hitler has the Army swear oaths of loyalty to him personally. Hitler further stamps his control on the Army by forcing out generals Blomberg and Fritsch in 1938.

However, the older breed of WWI-era officers who took this independence seriously are long gone by then - the new generation, who have by this point become accustomed to a Germany that exalts the Army and its political leadership were less concerned about the independence except insofar as it was an excuse to shut off any thoughts of disloyalty. Von Manstein, during WWII, for instance, refused to join the July plotters by saying "Prussian field marshals don't mutiny", forgetting about one of the Prussian state's finest hours, when General Yorck did, er, mutiny against Napoleon.

By December 1938, the Army even begins political training in National Socialism for all its personnel. During WWII - especially at the outset of Barbarossa - the Army makes many proclamations that are dripping in Nazi theory. About a third of officers are Party men by 1941.

The end result was a politicized organization that was loyal to the Nazi party and co-responsible for the Nazi's crimes. The "independent state within a state" tradition was dead by 1934, and it survived only a mirage for accused Wehrmacht war criminals and their latter-day apologists to conjure to try and obscure their crimes, and as a comfort blanket for the tiny minority of really apolitical officers to cling to if they found themselves questioning their loyalty to Germany.

As for other branches: the Luftwaffe and Navy were very similar, being parts of the Wehrmacht along with the Heer [Army].

The Waffen-SS was the armed wing of the party, naturally its personnel were mainly party-members - certainly the vast majority of men in its most infamous formations would have been. However, a good number of the later war recruits - who were mainly foreign askaris - probably never got round to filling out a party card; I doubt some of them were even eligible for party membership.

TL;DR: No, but they didn't need to be because they were loyal to the Nazi regime, and many did choose party membership anyway.

Membership within the NSDAP was not compulsory within the Third Reich. 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.