It’s complicated. Officially, after WWII, there was the process of Denazifaction for every adult to go through. Everybody was obliged to list their membership in Nazi organisations, and would then be evaluated by the board and placed into one of several categories ranging from innocent/ resistance over Mitläufer (minor follower) and Nazi up to war criminal. Depending on the status, a monetary or prison fine and limits for further political service were handed out.
In practise, when they started with the small fry, found out that evaluating millions of people after a war and the refugee situation from the East had destroyed a lot of records (and people destroying incriminating evidence themselves), it was impossible to find out if somebody was lying. It was also popular to get a priest or similar to issue a “Persilschein” (Persil was a popular laundry soap) that you were innocent. Sometimes this was a deal for food (people were hungry to the point of starvation in the later war years and afterwards till the money change), sometimes it was a tit-for-tat of two guilty people giving each other clean papers.
Added to that was the practical problem that if all offical Nazi members would have been removed from all political or admin. positions and put into prison for the next several years, the country would have been shut down, because you can’t take away the majority of the admin. in every town and city.
So most mid-guilty people were declared to be less guilty as followers.
And a lot of real high-ranking Nazis just kept their mouth shut and in the rush to rebuild the country both physically and politically (a Restauration set in under Adenauer, helped partly by the desire of the Americans to recruit the new West Germany as ally in the cold war, so exposing and arresting more Nazis was counterproductive for them, too) they rose to high positions.
It needed the next generation, the 68 students revolt, to ask questions of their fathers generation “How could you allow this to happen? Why didn’t you resist? What did you do in the war?” and demand that Nazi judges and Nazi politicans be thrown out of office.
The general view is that, while normal people were drafted into the normal Army (Wehrmacht) without a choice, to end up in one of the SS divisions, you had to apply specially and fulfill special requirements (purity of lineage). Therefore members of these special groups are considered more Nazi than normal veterans. (With the caveat of things being more complicated because regulations changed as the war went on. In the last days, the Volkssturm was called, drafting men over 60, disabled, and teens of 15 years. Technically, these teens could also be considered veterans for serving a couple of days before the surrender, but I have never heard of that.
They also used divisions of Hitler youth as helpers at the Flak (anti-aircraft guns), see infamously Pope Ratzinger and the discussion about this).
Practically today, (besides the mentioned biological solution as people get older and older), people keep quiet and pretend to be normal veterans. A few prominent ones have been tried as war criminals, sometimes late (Nazi crimes were exempt from the expiration of process on purpose).