Thanks, your obvious question prompted me to take another look at that issue. My first thought was “Yes, but it’s not quite there because…actually, why?” Since I couldn’t come to a good answer anymore (because by now the AFD really seems just as bad as the NPD always was), I did some digging through the constitution-equivalent, the Grundgesetz.

1. Art. 20 specifies that Germany is a democratic and social state and clause 4 states that any German citizen has the right to resistance/opposition against anyone who seeks to abolish that order/construct, if other means do not work out (it’s not specified what kind of “resistance”, so armed resistance is also on the table, especially with the wording “if other means do not work out”)
2. Art. 21 states that political parties can be formed freely and that their inner structure must equate democratic base values. It also says that political parties which (in their stated goals or their behaviour) seek to disrupt or disable the free, democratic foundational order, or endanger the German Federal Republic, not only are illegal but also may not receive governmental funding.
3. Art. 26 states that actions which seek (and are able) to disrupt the peaceful coexistence of the countries (internationally speaking), especially the preparation of an offensive war, are illegal.

So, why is the AFD still not banned? I read through two or three news articles and it seems to boil down to a couple good arguments:

1. Currently the AFD has been given the classification of right-wing extremist, which could possibly threaten the democratic order. This allows the German intelligence agencies to insert so called Vertrauenspersonen (basically spies), whose function it is to gather as much evidence as possible and needed to support a ban of the AFD.
2. Evidence may only be gathered before, not during, a trial procedure. So unless you are absolutely confident that you have more than enough (or at the very least exactly enough) evidence, you shouldn’t initiate a ban-trial.
3. If a ban-trial fails, it could give the AFD additional support because “if the government, despite using literal spies, couldn’t find evidence to ban us, we can’t be that bad!”
4. Those ban-trials can take multiple years to go through. During that time, the AFD could gain the support of impressionable, but not yet swayed, people by claiming “Omg, we told you! They are trying to ban us for speaking the truth! Please, help us against the oppressors!” (if you’ve seen the scene in Revenge of the Sith, where Mace Windu wants to kill Palpatine then and there, because he’s too dangerous and Palpatine goes “See, Anakin? I told you, the Jedi are evil!”, its basically that scenario)

I would be so happy to be rid of the AFD, but unfortunately it seems to not be a quick process :c