Was Fritz a Nazi all along?

During the course of Babylon Berlin's first season Charlotte's friend Greta falls in love with Fritz, who seems to be a passionate communist. Later in season 2 Fritz gets allegedly shot on the street by the police right in front of Greta and in her grief she agrees to help his comrade Otto plant a bomb in Councillor Benda's house, which ultimately kills him and his daughter. But when she is about to leave the city she recognizes Fritz among a group of NSDAP members demonstrating at the train station.

This confused me quite a bit and I actually see multiple ways to resolve this issue.

At first I thought that the the obvious solution is that the whole thing was ultimately a ploy and Fritz was indeed a member of the NSDAP all along and the whole love story as well as his death were staged to pressure Greta into helping them kill Benda. In retrospect this might give minor dialogue pieces from earlier in the show a new twist, like when they're introduced:

Fritz: Mass executions are a legitimate tool of the revolution.
Otto: Says who? Hitler?
Fritz: Lenin...Expropriation, too, by the way.

Or when Otto calls Benda a "Jewish pig" or something similar. I didn't make much out of this, since Benda seemed to be subject to antisemitic criticism from various sides in general and it might just have been a personal comment from Otto. But in retrospect it might have been a hint.

So maybe he was a Nazi pretending to be a communist in order to trick Greta.
But this would have meant that the whole thing was planned quite far ahead, since Greta didn't work for Benda right away, unless Fritz was already pretending to be a communist earlier for whatever reason.

But when thinking more about it, I wasn't even sure if the show ever clearly showed Fritz to be a communist. Seeing how the Nazis and the communists might superficially seem similar in some of their radical ideals, I considered it might even have been a clever ploy by the show itself to trap the audience into thinking he was a communist simply by confusing the matters and keeping it vague, like they did in the dialogue excerpt above.

So it could have been the show that tricked us (or me?) into thinking he was a communist.
But in addition to that there's also the problem that the reporter on the radio says that

For the cowardly and insidious attack on Councillor Benda and his family, an unknown faction of the Communist Party has taken responsibility.

So why would the communists take responsibility for this attack? Was that just to "cash in" on the event because they were currently in a conflict with the police over the shootings on May 1st? That wouldn't make the communists look particularly peaceful either, though. Or was that blame just fabricated by the police in order to have the moral upper hand over the communists in that conflict (it's quite comfortable that it's an "unknown faction" of the party)?

And last but not least, I really don't want to go as far as saying that Greta might just have imagined seeing Fritz among the NSDAP group. She does speak to him, but he claims she mistook him and pushes her away. It might go a little too far for that to just be Greta's imagination (especially since I'm already unsure about two other unrelated character returns in the very same episode), but it doesn't help to shed a clearer light on the situation either.

So maybe he is actually dead and it was the communists (or whoever) who killed Benda.

Now, that's become quite a long question but I wanted to make sure to lay down all my considerations to explain why I'm still confused about this. Maybe it was supposed to be confusing or maybe I'm just making it more complicated than it is. But I'd like some clarity on what was really going on with Fritz. Was he a Nazi all along? Was he pretending to be a communist and it was all a ploy to get to Benda? Or was it left deliberately vague to trick the audience? Is he even still alive at all? Or are we just unable to really tell what's the deal here?

_{(I'd also be willing to accept that only the next season might be able to shed a clear light on this, but seeing how the first two seasons are somewhat self-contained and the next ones weren't even planned until later, I'd be rather sure that the hints for this are to be searched in the existing material.)}

Best Answer

Okay, so I think you're on the right track.

I didn't see it until the second time I watched the show, but we actually see Fritz join the communists in episode five of the first season (or the only season, depending on what your localization is on Netflix or wherever you've watched it).

While Volker gives a speech in front of the Castle, Fritz actually walks up, reads a pamphlet and asks if he can join. Afterwards, he walks into the crowd and starts chanting "Murderers, murderers," with the rest of them.

Upon seeing this, I started to put things together better, so here's my theory, which is a modified version of your first theory:

Fritz has always been a Nazi. He joins the communists to create trouble and find ways to get the communists and the government into a more serious conflict. The discussion between Otto and Fritz does seem to indicate that they both read Hitler as well as Lenin and others.
Fritz did not plan on using Greta originally. Meeting Greta was chance, luck, and the plan to kill Benda only developed later.
Fritz, Otto, and other Nazi party members decided to fake Fritz's death. Greta never goes to the hospital, Fritz disappears immediately after being shot, and Otto is the only one who tells her Fritz has died.
Otto is Greta's handler. In order to manipulate Greta, they needed someone who could convince her that Fritz's death was at the hands of the political police, and they needed someone to keep in contact with her so they could kill Benda.
There are other Nazi infiltrators in the communist party. These members are the "faction" that claims responsibility for killing Benda.

So, in answer to your questions: Fritz has always been a Nazi. The ploy only developed after he got to know Greta. The show was deliberately vague--in fact the show is often deliberately vague and needs to be watched twice or even three times to catch everything. I didn't catch the real identity of Schmidt the first time either. Finaly, Fritz is definitely still alive, and I think it's quite likely we'll see him in the next season (which releases in late 2019, so I'm thinking the US won't get until mid 2020).

That's about it!