You bring no arguments I could ignore. You only make assumptions and claims.
How do you even come to the conclusion BSW was authoritarian (that describes the use of (or desire to reach) a strong central power the rejection of political plurality) or left wing (which is defined by striving for societal progress and especially equal rights and equal chances for everyone, which BSW denies migrants).
and mostly a east Germany phenomenon.
That is something you never brought up before. What point do you think you make with this phenomenon?
they will probably sit left from the view of the podium.
Where you sit usually concurs with your political positions, but does not define it.
If we'd take the Horseshoe theory again
Why should we, since it's debunked?
Another takeaway is that they are absolutely a threat to democracy,
Again something you claimed but never supported with anything.