Part I

Modified from an earlier answer of mine

This is a somewhat thorny and complex issue and one in which the answer will vary over time. The attitude of the Heer officers, and to a lesser extent Luftwaffe and Kriegsmarine officers, to their colleagues in the Waffen-SS was multifaceted and could be quite acrimonious. One component of 20 July plotters was to blame the SS for Hitler's assassination and immediately incorporate Waffen-SS formations into the Heer. The Valkyrie's plan any senior Waffen-SS officer that was reluctant to follow the new regime was that "they are to be taken into protective custody and replaced by army officers. Prompt and energetic action must be taken, with superior forces, to avoid serious bloodshed."

Part of this wartime antipathy towards the SS and its armed formation stemmed from the rather clunky command arrangement in which SS and Waffen-SS formations were subordinated to the formal military leadership on military affairs, but followed their own chain of command for security and ethnic cleansing operations. This problematic command arrangement came to the fore as early as the invasion of Poland. On 18 September, members of the Waffen-SS unit Leibstandarte Adolf Hitler executed fifty Jewish prisoners. Although this formation was under the command of the 10th Army, its Heer commander von Reichenau did not give the order for the mass shooting, and contracted is superior for clarification, von Rundstedt who in turn telephoned Hitler directly. Hitler informed von Rundstedt that these actions fell under Himmler's responsibilities and not the military's. Hitler had authorized the SS to take command of issues of security and pacification in the wake of the German invasion, a task that the SS heads Himmler and Heydrich were quite willing to accomplish. Although there was some discomfort among Heer generals about the morality of these actions, most notably Colonel-General Johannes Blaskowitz who filed a formal protest against the SS-led Einsatzgruppen's actions in Poland, most of the dislike for the SS's methods stemmed from the fact that they often fostered a spirit of indiscipline among Heer troops brought in to supplement the strength of these security detachments. There was little to no sympathy among the upper-echelon Heer officers for the victims of the SS's actions. Even Blaskowitz at a February 1940 OKH meeting framed his opposition to indiscriminate murder as something whose main victim was the perpetrators, because "inordinate brutalization and moral depravity that would very quickly spread like a disease through worthy German human stock." But this friction between the Heer and SS ensured that the Einsatzgruppen played no role in the Western European campaign, a gesture to the Heer that so frustrated RSHA head Heydrich so much that he appealed to Himmler to be temporally deployed to the Luftwaffe for the Norwegian campaign.

There were other aspects of the Heer acrimony towards the SS that only grew sharper as the war progressed. The activities of the Einsatzgruppen reflected the larger bureaucratic ascendancy of the SS in controlling and running the resources of occupied areas, especially in the Eastern Front. The primacy of the SS over Eastern settlement complicated the organization of Eastern Europe's occupation economy. This meant that the Heer often had to run through the gamut of SS bureaucracy in these rear areas to gain access to the material and human resources under German occupation. Things were slightly different in Western Europe in which the Heer tended to hold primacy over the occupation regime, but often had to play a bureaucratic cat and mouse game with the SS from encroaching on their territory, either through the SS's increasing monopoly over the Reich's internal security or the organization's courtship of various fascist and anti-communist Western Europeans, which in turn provided the nucleus for the some of the foreign Waffen-SS formation. The expansion of the SS formations, both Waffen-SS and its various foreign auxiliaries also caused considerable consternation at a time of acute shortages of equipment and personnel. Despite their postwar reputation, especially in the West, as a military elite, the combat performance of the Waffen-SS was not especially superior to other German formations. Yet the Waffen-SS formations tended to get far more military equipment than their Heer analogues. Waffen-SS divisions had a higher establishment figure than Heer divisions (ca. 20000 vs 16500) and a much greater degree of motorization. Although the Waffen-SS was to be a volunteer formation, the SS often flaunted its recruitment limitations set in agreement with the Heer. The fact that the SS also became the ideological face of the Third Reich's military forces also meant that it tended to siphon away a number of the best of the new levies. A number of Heer officers tended to disparage the professional capabilities of Waffen-SS officers and critiqued their lack of knowledge of the finer points of military science. Fedor von Bock noted in his war diary in the Spring of 1940 after visiting a SS motorized regiment under his command that:

The combat training of the non-commissioned officers and men of the SS is inadequate; it will cost a lot of blood! Shame about the splendid manpower material.

Field Marshal von Rundstedt would once castigate SS-Oberst-Gruppenführer Sepp Dietrich's inability to understand the military situation even with the help of a map. In a February 1943 inspection of SS-Leibstandarte division, Major Ulrich de Maizière echoed von Rundstedt's disdain for the Waffen-SS's military dilettantism:

The commanders of this Waffen-SS division did not seem to realize that brave and ideologically misguided young men were being senselessly sacrificed through insane arrogance and a lofty disdain for sound training. Belief in the Führer was more important to them than professional ability. Shocked and sobered by the experience, I returned to headquarters where I was given an opportunity to report my impressions to the chief of the general staff.

From the Heer's perspective, the SS was denuding the regular army of its best potential replacements and equipment and in return providing the German military effort with subpar or average material.

The underlying cause of this unique situation was that the Waffen-SS's expansion was reflective of a phenomenon common to dictatorships called a "parallel military." A parallel military gains strength through proximity to the dictator, ideological compatibility with the regime, and capitalizes on the need of the dictatorial state to have special military formations to deal with the enemies, real and potential, of the state. The war gave the SS an opportunity to expand much greater than the Heer officers were comfortable with and within the wartime Third Reich, the SS emerged as state within a state. The expansion of the Waffen-SS led to the creation of its own training establishments and procurement offices that operated independently of Heer control and observation. Its ability to recruit among occupied Europe underscored to many Heer officers that the SS had an outsized importance in German occupation policy. The SS's RSHA office was already planning for the reorganization and population policies of Poland, the Baltics and USSR, which was a clear signal that if German arms triumphed, the Heer might not enjoy the full fruits of victory in the new order. Knowledge of the SS's ascendancy rankled many Heer officers as the polycratic Third Reich was predicated upon competing power blocs "working towards the Führer," and the trends in both the prioritization of equipment and resources was a sign the Heer was losing that bureaucratic battle while bearing the bulk of the war effort.