I'd like to cut short my ramblings, the next will be kinda true (as I see it) from the regime change to this day.
In the '90s narration changed. In lyrics the way of life, existential stuff got more space, all bands distanced themselves from political parties, but ofc daily politics reached to them too, and their punk listeners ofc political beings too. Some anarchists remained, but the new generation of punks often chose a softened position, supporting Munkáspárt (Labour Party), and communism in general. Bands sometimes covered communist songs, maybe for nostalgia, maybe sarcastically I dunno what were their reasons. The outrageous lyrics remained, vulgarity for the sake of vulgarity, just as well Kleinbürger shaming. Humour found it's way too, at least I heard songs I could smirk at. Also sex, drugs r'n'r as always, rebelling against traditions/empty habits and authority. Basically they summed up all the wisdom a kid in his late teenage, early '20s should know.
The music got a little more polished, especially among those bands who's stuff got to wider audience, those whose listeners were not entirely from the subculture.

HétköznaPICSAlódások (Everyday Disappointments)
The words are written in one so one can read PICSA in the middle, which means pussy/ass. Often mentioned band, heard only a couple of songs of them, for some reason.
Commandante
https://youtube.com/watch?v=2a695Y2LNdQ [Embed]
Ájn, cváj, dráj (One, two, three)
https://youtube.com/watch?v=HbLN7wq7MuQ [Embed]

Prosectura (Morgue)
I consider them a joke. Probably they do too.
Tahó család (~Stupid family)
https://youtube.com/watch?v=Mr2vq8tJU4M [Embed]
Kimegyek a szigetre (I visit the Sziget) - about the Sziget Festival
https://youtube.com/watch?v=m9hHB1Yd0As [Embed]