Was every soldier a Nazi? Of course not. We try to stay away from words like "every" in history, because all it takes is one counterexample to disprove something. According to Omer Bartov, 29% of senior Wehrmacht officers were members of the NSDAP as of 1941, and the figures were similar for junior officers. I don't know of any source that has calculated specific figures for enlisted soldiers, unfortunately; however, the peak membership of the Nazi Party was about 8 million and there were about 18 million Wehrmacht personnel, so Nazis were certainly in the minority in the Wehrmacht's rank and file as well. Hitler actively promoted the Nazification of the military, gradually eroding the influence of the old Prussian noble elite, particularly in the later years of the war, when the numbers of Nazi-trained officers increased; however, it should be noted that the existing military elite wasn't a bastion of resistance to Nazism, and most of its members actively participated in planning and executing war crimes.

In any case, the more important point is that regardless of the exact membership numbers, Nazi ideology thoroughly penetrated every level of the Wehrmacht hierarchy, from the High Command (OKW), to the officers, to the rank-and-file. Officers and enlisted men were subjected to intensive propaganda, particularly during the war against the Soviet Union, which was explicitly framed as an ideological and racial war of extermination (Vernichtungskrieg). Bartov argued that Nazi propaganda and sincere belief in the Nazi racial-ideological cause made the Wehrmacht a stronger fighting force by promoting group cohesion that wouldn't have been possible in a less politicized army. This cohesion was reinforced by harsh discipline and a draconian military justice system, which punished "subversion of fighting strength" (Wehrkraftzersetzung) with execution, imprisonment under harsh conditions, or service in penal battalions, which was tantamount to a death sentence. So, even non-ideological soldiers had incentive to fall in line.

Regardless of whether they had NSDAP membership badges or not, Wehrmacht personnel at all levels were active participants in war crimes and crimes against humanity. The OKW issued orders which they knew were violations of international law, including the Commissar Order, which called for the execution of Soviet political commissars and Jewish POWs; the Barbarossa Decree, which called for harsh reprisals (including summary execution) of civilians accused of resisting the German occupation; and the Severity Order, which endorsed the mass murder of Jews. Wehrmacht officers and enlisted soldiers took part in the mass murder of Jews, partisans, and POWs, and the Wehrmacht administered a POW camp system in which 3.3 million Soviet POWs died, mainly due to disease and deliberate starvation.

It's impossible to generalize about a group of people as large as the Wehrmacht; you can't speak collectively about the beliefs and motivations of each member of a group of 18 million people with any empirical rigor. But the outcomes of the Wehrmacht's actions make it clear that, whether they were committed Nazis or not, German soldiers at all level of the chain of command participated in the war of extermination and the Holocaust, and were responsible for the deaths of millions of civilians and prisoners of war. The idea of a clean, non-ideological, apolitical Wehrmacht has been thoroughly debunked, even if actual Nazis only made up a minority of its personnel.

Sources:

Omer Bartov, The Eastern Front, 1941-1945 (St. Martin's, 1986)

Wolfram Wette, The Wehrmacht: History, Myth, Reality (Harvard UP, 2007)

Jürgen Förster, "The Wehrmacht and the War of Extermination against the Soviet Union," in Michael Marrus, ed., The Nazi Holocaust, Part 3: The "Final Solution" (Meckler, 1989)

Christian Streit, Keine Kameraden: Die Wehrmacht und die sowjetischen Kriegsgefangenen (Dietz, 1997)

Hannes Heer and Christian Streit, Vernichtung im Osten: Judenmord, Kriegsgefangene und Hungerpolitik (VSA, 2020)

These questions may be of interest to you:

• How invested in Nazi ideology was the average German soldier?
• Is saying that a Wehrmacht Heer soldier was a Nazi the same as saying a US soldier is a Republican or Democrat? Is it known how many German soldiers opposed the German government and tried to leave or even join the Red Army?
• Why did the Nazi government require Wehrmacht soldiers to be apolitical when every other branch of society was being politicized?, /u/kieslowskifan
• Calling German soldiers "Nazi's", correct or incorrect?