During the cold war and after, the US and anglosphere was mostly interested in the destruction of left ideology, labor unions, left parties etc. were all targeted. The right offers a safe outlet for people with those grievances, it doesn't threaten capital, so it was always allowed to linger in Germany not just in the east. It's deeply rooted in establishment and civil organizations, in university fraternities (schlagende verbindungen, the CSU etc.). The allied supported and used and bolstered far right groups all around Europe (Gladio, NSU, etc.) in their fight against socialism and people on the left. We still feel the effects to this day and state and federal police and intelligence still operate this way.
Protests in Germany you see police protecting far right groups from leftists, not the other way around. It's a necessary aspect of liberalism to allow the disenfranchised the outlet into right wing extremism.