There were probably several factors at play here:
- The Bundeswehr saw the Wehrmacht as a respected predecessor.
- In the 70's you still found many influential officers, politicians, judges and other 'pillars of society' that had been Nazis, still were Nazis at heart, or had been active and successful in the Third Reich in some way. Maybe, they did not see honoring a war criminal as outrageous.
- The whole public discourse around Nazism still centered on small group of perpetrators.
In the early years of the Bundeswehr, there have been debates about what traditions this army should hold, given that the two predecessors - Reichswehr and Wehrmacht - had a problematic history, to put it very mildly. Many higher officers saw a vital need to maintain traditions and saw the Wehrmacht as a positive point of reference. There's a decree, the Traditionserlass that tries to codify this relationship. The Traditionserlass notes Stauffenberg & Co. as positive examples from it first edition in 1964 on, while avoiding a clear statement on the Wehrmacht. The current version, from 1982, contains the sentence that the Wehrmacht can not be a foundation for traditions. Individual units however may and are held up as exemplary. So in the 70's, parts of the Bundeswehr saw the Wehrmacht as an important part of their traditions, so they would honor an old soldier.
In the decades after WWII, a prevailing attitude in Germany was that the German population had been 'seduced' by Hitler to start WWII and the Holocaust, and that only a small circle of perpetrators was actually guilty. This included the belief that Wehrmacht had been fighting 'honorably', and that the SS was to blame for the atrocities. Remember, Goldstein's " Hitler's willing executioners ", which would be the starting point for a wide ranging debate on the role of ordinary Germans was only published in the 90's. The 90's was also the time when the exhibition Vernichtungskrieg: Verbrechen der Wehrmacht toured through Germany sparking debate on the role the Wehrmacht had played in the atrocities committed by Nazi Germany. Public discourse had not been as hostile towards the Wehrmacht in the 70's.
IMO, military honours for Mannstein are inexcusable. The Guy had followed the Kommissarbefehl and 'inspired' his men to murder Jews. It is indicative of the public discourse in Germany in the 70's and the conflicted relationship the Bundeswehr had to the Wehrmacht.
Edit to Add: For a contrasting case, look at Admiral Dönitz: In 1945 he was head of the Navy and, for the short time between Hitlers Death and ermany surrender, Reichpräsident. He was also very much a Nazi. In 1969, General Inspector of the Bundeswehr Ulrich de Maziere suggested to the then Minister of Defence that Dönitz should be buried without any military honours, because according to him "you can't separate the soldier Dönitz from his bahaviour around and after 20.7.1944." There was some to and fro over the following decade (would serving officers be allowed to give speeches and similar question) but the order was in effect in 1980 when Dönitz died and was buried without military honours.
So in one case a political decision was made to not give military honors to a convicted war criminal.