As with many insults, I would guess a lot can be packed into the particular circumstance and sneer that comes with the epithet. Straight out of college, late 1970s, I went on a tour of Europe arranged by one of the professors at the University of Illinois.
Long story shorter, we stayed a few days in West Berlin, and had a free day to cross into East Berlin. At the customs station, I was standing in line near another member of our tour, a young black woman. There was no direct incident, but when we got though, she said that she spoke German, and was annoyed by what she heard one of the agents call her, simply “Ausländer”. I speak a little German, and I was puzzled: I could well believe that insulting Americans came easily to those agents, but as far as I knew, the word simply meant ‘foreigner’. She said, no, that under the circumstances, it also had a racist tone.
Ausländer specifically means ‘foreigner’, though. It is used in a precise way to mean person of citizenship other than German (prior 1913, including persons from another German state), and used loosely by bigots: person of non-German ethnicity. So it does not mean ‘outcast, reason for being so unspecified’.
Non-German citizenship or ethnicity is also not a believable reason for your protagonist to be an outcast from the whole town, as opposed to being disparaged by a few bigots.
Would it serve the purpose of your narrative for your protagonist not being objectively treated like an outcast, but just to feel an outcast? In that case it would suffice for him/her to be an immigrant from a country where baseline politeness means to love-bomb a new arrival. In German culture politeness means leaving people alone and giving them space (negative politeness), which makes people from more demonstrative cultures feel being given the cold shoulder.
Aussätziger, maybe? I would translate it as “outcast”, even thought the original meaning is about someone who is an outcast due to medical reasons (leprosy, etc.).
A somewhat antiquated term would be der Geächtete, which is somebody who is specifically ostracized from society due to some crime/transgression they committed. They’re stripped of the rights and protections conferred by being a member of society, so essentially forced to fend for themselves. Related terms are vogelfrei or wolfsfrei, which one might think to mean something like ‘free as a bird/wolf’, but derives from the practice that their bodies aren’t buried, but left to the carrion eaters to pick clean. (So it’s a free meal for the birds and wolves.)