I've only been reading this sub for about a week, but I know the issue of the Wehrmacht (German Regular Army) on the Eastern Front has been covered before. Suffice it to say, there have been a lot of studies that illustrate the ideological motivation of these soldiers and their willing participation in the more ethically unsavory actions that occurred on behalf of the Nazi war effort on the Eastern Front (the massacre of civilians and POW's that you reference). The attempted refutation of this is often called the myth of the "Clean Wehrmacht" and my understanding is that it has been almost totally repudiated by scholarly consensus.

The study I am most familiar with is Omer Bartov's "Hitler's War", which seeks to (quite convincingly I might add) convey to the reader that the Wehrmacht, from its officer corps to the ordinary soldier, was almost invariably committed to Nazism's ideological goals either through explicit statement, or tacit participation in the atrocities. I don't recall any instances of protest by German soldiers (much less an organized group) against their methods of warfare in that book.

The only work I know of that presents something of an opposing viewpoint to this is Christopher Browning's "Ordinary Men" which is a more narrow study of one German Army unit in Poland participating in the Holocaust. He gives a more "following orders" sort of narrative to the atrocities and cites a high rate of alcoholism, suicide, and mental illness among the men of the unit. Even so, guilt does not equal refusal and, again, there's no instance of a soldier not following orders or organizing resistance that I can remember in that one either. EDIT: I unintentionally misrepresent Browning's work here- refer to the post by /u/NeuralLotus in reply to mine for a better analysis.

This thread contains a similar question to yours and there's a lot of really good answers there that expand upon my own here. If a specialist wants to step in here and correct/modify my answer that would be great because it would be rectifying my own misconceptions! I gave this answer, though, in an altruistic effort to give WW2 specialists/mods a break from a common question that's been asked in different forms. Anyway, I hope that helps!

It is a complex question because the Wehrmacht was in many ways a hotbed of opposition to Hitler, but this opposition was often narrow and muted. The Wehrmacht was dominated by an officer corps made up of conservative Prussian aristocrats. Though they supported Hitler's rise to power in the early 30's, there was consistent opposition to Nazism that was allowed to continue in the army that reached a climax in the July 20 plot. Senior German officers allowed a wide range of political thought to percolate among their subordinates and the army maintained a large degree of independence from the Nazi party. This opposition however was more rooted in the army leadership having its traditional role in shaping the larger course of German foreign policy, as both an institution and a social class, undermined by Hitler and his underlings in the party. It was generally not an ideological opposition and it was limited by the conservative nature of those involved, who felt bound by their oath to Hitler and also constrained by his enormous popularity.

Also rooted in old Prussian conservatism was a belief in the inferiority of the Slavs and the peoples of the East. Prussia which formed the nucleus of modern Germany, was founded by the Teutonic order of Knights who violently displaced and assimilated the pagan Slavs of the Baltic coast. Later in Prussian history there was also racial tensions as Prussia gained new territories in the partitions of Poland throughout the late 18th Century. There was a violent series of land appropriations and forced cultural assimilation. Further, Russia was long seen as an existential threat and had come very close to destroying Prussia outright in the Seven Years War.

German national identity and the territorial space in which it existed was still being actively constructed all the way into the 20th Century and there was a widespread anxiety and even a certain siege mentality among many Germans that predated Nazism. So while the army was more of a throwback to the old Germany and wasn't indoctrinated in rigid Nazi racial policies; the idea of creating a living space in the East and dealing with the people there harshly resonated very strongly. There was some opposition to Barbarossa, but it was seldom over Nazi racial policy or moral concerns, instead it was based on skepticism regarding its strategic necessity or its chances for success. The only organized resistance on moral and philosophical grounds centered around the Kreisau Circle to which people like General Ludwig Beck and many former and current army officers belonged but they were only a small minority.

I would suggest reading Barbarossa: The Russian-German Conflict, By Alan Clark. It goes into some wonderful detail of the dynamics between the Wermarcht, Hitler and the Nazi Party during the war in the East.

The truth is in short; hard to tell. Enlisted man's memoirs and correspondences seem to be more concerned with talk of home and hearth and reminiscing. Their post war statements are to be categorically dismissed; ideas of 'the Great Trap' and psychological victimization means that survivors of the Ost-Front are immediately suspect. If you want any further evidence, read Otto Carius' 'Tigers in the Mud'; an excellent book, but absolute trite when dealing with the issue of the German invasion of the Soviet Union and the German soldier's complicity in his regime's crimes.

Now, did soldiers - period end - question the atrocities? Yes; there seems to have remained a handful of Wehrmacht Officers of the old order who realized they were not only Army Officers, but flagbearers of the German state and how others perceived it. Many anti-Nazi elements existed in the German military and not all stood silently by.

A few examples of convenience I'll take from Beevor's Stalingrad (which I just happen to be re-reading); I will quote some things the author lifted from Col. Helmuth Groscurth - a convinced anti-Nazi and member of the July plot to end Hitler's life.

Page 16: When the illegal Barbarossa orders were prepared [Commissar Order, Orders for Co Operation with SD], in March 1941, two opponents of the regime, the former ambassador Ulrich von Hassell, and General Ludwick Beck, were shown copies of these secret orders by [Then Lt. Col] Helmuth Groscurth...'It makes one's hair stand on end', wrote Hassel in his diary, 'to learn about measures to be taken in Russia....this kind of thing turns the German into a type of being which had existed only in enemy propaganda.'

Groscurth and his fellow plotters and sympathizers come up time and again, excellently illustrating the point, for example following Groscurth's attempt to halt the killing of ninety Jewish children (page 56):

"Groscurth wrote a full report which he sent direct to headquarters Army Group South. Appalled and furious, he wrote to his wife: "We cannot and should not be allowed to win this war." At the first oppurtunity, he went on leave to Paris to see Field Marshal von Wiltzleben, one of the leading members in the anti-Hitler movement."

There are further, revealing quotes, but I'll leave it at those two, both which show Groscurth was not alone in the field or general officer classes in both his disdain for the Nazi regime and their deplorable ideology. Men directly under his orders, and likewise for other anti-Nazis, never received copies of the Commissar order or the Sonderkommando co-operation bulletin, which had been handed down by higher leadership.

However, the few stand out for the exact reason that they are the few. Myself, and others, have gone to great lengths to explain the indoctrination of the German soldier. Post-war interviews reveal how thorough it is; responses are 'we feared communism!' or 'we were just doing what they would do to us!' are not uncommon. Few German enlisted would've really cared about what was going on around them, and I'm sure private misgivings have been lost to the sands of time.