Sort of a tongue-in-cheek follow-up question. Could you be fit early 20s Jewish man and serve in the military and is there any difference in the service required? I'm thinking analogous to African Americans serving in WWII.
It was possible and there were several reasons why someone in the demographic you described would still be in Germany.
The first and most obvious was – like in so many draft systems – the question of the job one held, had been trained for or were in training for. Nazi Germany had the term "unabkömmlich" – indispensable – for people whose jobs and positions had been deemed indispensable for the functioning of the German political, administrative and economic system and who accordingly would not be called up to military service. The "unabkömmlich" designation encompassed a rather large number of jobs and positions: From skilled workers in factories producing munitions and/or weapons to huge swaths of the German civilian administrative apparatus, both in Germany as well as in the occupied countries to people in the internal hierarchy in the Nazi party, such as your local Nazi Party leader – for how could Germany fight a war without the party officials there to indoctrinate the populace.
However, who was unabkömmlich and which jobs were in principle designated as such changed over the course of the war. Germany during WWI suffered a massive man power problem. Already in the late 1930s, the German economy began experiencing a severe man power shortage. This was among the prime reasons why the Nazi regime implemented a major escalation of policies and measures of persecution that also affected German laborers during that period. The persecution of so-called asocials, the cooperation between well-fare agencies, labor agencies and Gestapo, the expansion of the Concentration Camps system with camps such as Buchenwald and Mauthausen build around that time are all best understood in the context of the Nazi state trying very hard to mobilize labor reserves through massive imprisonment. Similarly, around the same time the labor agencies were granted a massive choke hold on German workers. Form 1938 on you couldn't just change your job anymore but rather had to get permission from the labor agency, who had also the possibility of sending laborer that in the eyes of their employers didn't conform off to so-called "labor education camps", a Gestapo camp where people were imprisoned for 40 to 60 days.
The reason this is important is because during the course of the war, the regime's strategy was to replace more and more German workers with foreign forced laborers in order to free up the former to serve in the Wehrmacht. This invariably changed which jobs and professions were deemed unabkömmlich during the war. For example, following the German occupation of Poland several hundred thousand German soldiers from agrarian families were released from the Wehrmacht as reservists in order to help their families with the harvest. Many of them remained out of the Wehrmacht and away from active service until the invasion of the USSR in 1941. Once that occurred however, this policy of releasing hundreds of thousands of agrarian laborers from the Wehrmacht stopped because over the course of the war with the Soviets, unskilled agrarian laborers in Germany were simply replaced with Polish or Soviet forced laborers. Over the course of the war, 15 million people came to Germany as forced laborers with 1944 seeing the peak of this massive system when the German economy employed 7 million forced laborers in the month of August. That was almost a quarter of the entire labor force in Germany.
So, a person could be deemed "unabkömmlich" when they couldn't be replaced either by someone of similar qualification working twice as hard or by a foreign forced laborer. This included skilled factory workers like machinists and certain tool makers but also – important for the demographic you are asking about – university students. Although the number of university students had due to political and demographic developments been shrinking during the 1930s – with the lowest number being 28.696 university students in all of Germany in 1939/40 when many volunteered for the Wehrmacht – it still was a significant population that for the most part could earn a significant deferment. While some students such as medical students or those working on research significant for the war effort by way of armament projects were for the most part excused from serving until very late in the war, for many other students their status meant that they were called up to serve only for a short time. Take f. ex. Hans Scholl of White Rose fame: He served on the Ostfront for 15 weeks in 1942 after already having received his military training in the 1930s and having enrolled as a student during the war. Entire student units existed wherein university students were commanded to serve at the front during the semester breaks.
And while these were all "run of the mill" reasons for why someone from the demographic you described might not serve in Nazi Germany, there was another significant population that wasn't called up: Jews and those imprisoned in concentration camps. For some of those imprisoned in concentration camps, service in the Wehrmacht could indeed be a way out of the camp or a way to free family from the camp. This is a phenomenon that can be observed, interestingly enough, with several members of the Romani community from Austria's Burgenland with regard to the Lackenbach concentration camp. There several men who volunteered for the Wehrmacht were able to free themselves and their families and ultimately save themselves from deportation to Auschwitz. Why this request was granted by the Nazi administrators and who made the decision about which prisoners could volunteer and which couldn't is unfortunately not documented but in a very limited number of cases it was possible.
Also, I've written about this before here but the Nazis' policy on homosexuals was not as comprehensive as it is sometimes imagined and not all persons arrested or even sentenced for homosexual activities went to Concentration Camps. In fact, many of them also served in the Wehrmacht either in lieu of their prison sentence or after their sentence had been served.
The only victim group of German nationality consistently not called up were those the Nazi regime regarded as Jews. Although, so-called Mischlinge, meaning people the regime regarded as "mixed race" were also drafted. While at several points in time the regime discussed getting rid of those soldiers, in the end that didn't happen, most likely because of practical considerations.
Related question: How was Wehrkraftzersetzung implemented? Was it applied very strictly?
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