The next I wish to introduce one from the early punk bands I know a bit more. Their music, I mean, not their history. I believe they are from the second wave from the early '80s but the two albums I heard (I listened only one "actively" tho) is from about 1990. One leg still in the authoritarianism of the communism, the other in the chaos of liberalism.
Btw this "first and second wave" thing is my invention, I've no idea if punk rock history has these categories or can be really divided into this, I just rationalize the thing that way.

Aurora
As far as I know they were also a kinda iconic band but never went mainstream. Their music is less raw than CPg's but not smooth enough for wider audience. The Viszlát, Iván! (Goodbye, Ivan!) album was born while the communist regime gave back it's soul to it's creator, the Előre kurvák gengszterek (Forward, whores and gangsters!) is about the new challenges of the new system, the politicians, unemployment, rising crime, fickleness of the future.
I also heard some later songs of theirs but I can't remember which ones.

Here's a cover of Bella Ciao, an (or The) Italian partisan song:
https://youtube.com/watch?v=A4Ra5YC7npk [Embed]

Viszlát Iván (= Goodbye, Ivan) - from the album the same title
https://youtube.com/watch?v=4TERe2nAKgo [Embed]
We love you, let's say our farewell, Ivan
The Stalin's organ whishes for a church song
Seryozha take home the letters of Tatiana
What we have learnt from you, it doesn't help us