The cold war has been over for a very long time. The whole process was reformed in 1984 by removing the mandatory oral hearing. Sources say that acceptance rate was above 90% after 1995. That's not good enough (should be 100%), but not terrible either.
For example, I don't think it's in my interest to defend or die for the German state. However, I would use violence to protect my life if someone tried to kill me or threatened my life directly. The German state would interpret this as a political objection rather than a conscientious one, since I am willing to use violence in principle. If I could convince them that I would let someone kill me without defending myself because I categorically reject violence for any reason, they might consider that a conscientious objection.
> Sources say that acceptance rate was above 90% after 1995.
Yes, as I said, after the Cold War, Germany no longer wanted to maintain such a large army, so they started accepting any reasonably well-written argument. But in any war, you can see that nation states will start struggling to recruit new soldiers as it becomes obvious to the population that it's a rather pointless endeavour to die for their state. So, they start forcing people. We've seen that in Russia, Ukraine, Israel, USA, etc.
That is a complete fantasy of yours. Political convictions are explicitly stated as a valid type of justification for conscientious objection by the Act on Conscientious Objection to Military Service. It even states the reasons do not have to be logical or objectively comprehensible, which easily covers your "I'm not opposed to all violence in all theoretically cases, but I fundamentally reject service for the German state".
That's one way to put it. The other would be 1 year of paid community service (which the alternative services ALWAYS were).
Also at that time only some people had to go to the draft, because they had not the capacity to take everyone. That made it likely easy for them to let go of suboptimal candidates.