However the Verfassungsschutz has a terrible track record when it comes to investigating and preventing right-wing attacks e.g. against asylum seekers and immigrants. There have also been several cases of dubious use of informants (at one point it was joked that the far-right party NPD is entirely run by informants) and intentional destruction of records.
Also Verfassungsschutz members have publicly spoken out against the dangers of left-wing extremism while being dismissive about right-wing extremism, the most recent case being the person literally in charge of the organisation who insisted that a video showing a group of people attacking immigrants posted on Twitter was likely fraudulent despite several news outlets vouching for its authenticity and providing fairly exhaustive evidence from their fact checking departments.
On a side-note: in communal politics, the right-of-center "majority party" CDU just formed a coalition with the far-right AfD, which had previously been a taboo and was officially ruled out by the CDU party leadership. So the risk of far-right extremism being normalised is very present and very real right now.
Nominally, this is to prevent the rise of another movement like the Nazis. But ironically, one of the first parties to be banned was one of the only two that had vigorously opposed the Nazis during their rise, the KPD. Nowadays, there are suspicions that the Verfassungsschutz is riddled with far-right sympathizers itself, given how it has handled several cases.