[grey-area]

The Stasi were the secret police for Eastern Germany, nothing to do with the Nazis as far as I know.

The surveillance undertaken by the Stasi wasn't really as extensive as (for example) collecting all phone records for the entire country, so in some ways the US has surpassed the Stasi in surveillance, while in others obviously it's nowhere near the same situation (e.g. in-person surveillance and recruiting ordinary citizens as spies), and in other areas it's similar - secret courts and sweeping warrants etc.

I suppose the point of the comparison is to shock, and then perhaps point out that there are some areas in which the current situation is worse than it was in Eastern Germany.

[rmc]

Given that communists and fascists have historically really really not liked each other, yes the secret police of communist East Germany, would not like each other.

(In East Germany, the Berlin Wall was called the "Anti-Fascist Barrier", and Nazis imprisoned and banned the communist party)