The CDU has a Prepper problem

[Middle-aged Europe]

The bigger issue is probably that while everybody was distracted by the rise of the AfD (in eastern Germany), at least parts of the East German CDU also started to move far to the right. Compared to their, let's say, more classically liberal West German counterparts in NRW, Hesse, or Schleswig-Holstein they've practically become a separate party of their own now, which has also caused more frequent friction between eastern state chapters and the head office in Berlin. See also the debate in Thuringia whether the CDU should form an alliance with the AfD there (with the AfD in Thuringia perhaps being the most right-wing state chapters of that party), something that hasn't materialized because it is constantly vetoed by Kramp-Karrenbauer.

Hot take: Hadn't the German reunification happened back in 1990, an independent East Germany would be governed today by a CDU-AfD coalition with the CDU actually more similar to Orban's Fidesz. However, since the East German CDU is subordinate to an all-German CDU and the East German states are subordinate to a federal government this has never materialized either.

I would also add that it is perhaps still a genuine German phenomenon that if you move further to the right you suddenly end up with full-on Nazis, with no (or at least less) intermediate steps in-between that seem to exist in other countries and their right-wing parties.  

[Middle-aged Europe]

are all "preppers" in Germany "far right" or just assumed to be?

Not necessarily, although the overlap between the two is large enough for the Federal Criminal Police Office to have conducted threat assessments of the scene in the past. At least one of the preppers in question here is confirmed to have been participated in the organization of a neo-Nazi rally in the past though (with neo-Nazis I mean actual Nazi Nazis, those who are to the right of the AfD). A bit more of a concern is probably the second part:

why would being part of a group that is a private support network for active and former soldiers and security personnel be something to be concerned about?

Because many of Uniter's members (including its founder and ex-leader) have also been found to be members of the so-called Hannibal network, and several of them are being investigated and/or prosecuted for various offenses including the preparation of terrorist attacks. As such, both organizations are suspected to be closely interconnected.

A private support network for active and former soldiers and security personnel would in itself be unproblematic as long as it isn't also a support network for criminal activities.

[Middle-aged Europe]

The bigger issue is probably that while everybody was distracted by the rise of the AfD (in eastern Germany), at least parts of the East German CDU also started to move far to the right. Compared to their, let's say, more classically liberal West German counterparts in NRW, Hesse, or Schleswig-Holstein they've practically become a separate party of their own now, which has also caused more frequent friction between eastern state chapters and the head office in Berlin.

Has there ever been talk of the East German CDU chapters joining CSU instead?

Not really.

But funny that you ask. In early 1990, the DSU (German Social Union) was founded in the still independent GDR with support by the Bavarian CSU. The DSU was supposed to be the sister party of the CSU in East Germany and ran there in the first and only free and democratic legislative election in March 1990, winning 6% of the vote and subsequently joining the CDU-led transitional government. Following the reunifcation the CSU bowed to pressure from the CDU and decided to discontinue their support for the DSU which quickly declined to the status of a splinter party. The DSU still exists to this day, although is pretty much politically irrelevant.

[Middle-aged Europe]

Yesterday, the CDU in Saxony-Anhalt had set an ultimatum for Robert Möritz (the prepper/ex-neo-Nazi who initially caused this whole debate to start) to explain his political past and credibly distance himself from any extremist ideologies in writing until the end of this month. Today, he has announced that he will leave the party altogether instead.