I think this is one of those areas of discussion where for me there’s a huge difference between a “hypothetical, ideal situation” and my current, specific one.

You're totally right! Hypothetically supporting having conscription in an ideal society is different from supporting it in a specific place and time.

I’m an immigrant from the Soviet region

Ich auch, aber wohne in der Staaten. Vielleicht verstehen wir einander deshalb )

But I just don’t wanna pick up a fucking gun for this ex Third Reich country that massacred my relatives.

The problem here is of course not conscription in Austria, but rather, like with everything else in life, the dissolution of the Soviet Union! Or, more abstractly, anyone having to move to a place that they aren't willing to fight for. I'd see no problem fighting for (denazified) East Germany, for example.