Overall great job, and i understand that you have to make some compromises in order to keep the rhyme scheme, but i would just make a few minor grammatical/stylistic adjustments to make it sound more like correct German:

Dass Für Banderas Horde muss das Volk jetzt frieren

["müsse" instead of "muss" would sound even more accusatory here, but it's up to you, both work]

Und die labern das von russischer "Aggression"

["labern was von" also works and sounds more mocking, just depends on the rhythm you want this line to have...]

Der Grund ist sei, dass sie die "Freiheit bedroh'n"

[It's important to use "sei" instead of "ist" so you don't sound like you are taking them at their word]

Arbeiter, Bauern, der Kampf geht nur nun weiter

[It's hard to explain why "nur" feels odd here, technically it should be correct, but it doesn't sound right; "bloß" could work too, but i prefer it with "nun"]

Die oben woll'n niemals mit Rheinmetall streiten führen

[This shortens the line and keeps the rhythm more consistent, and also it's a half-rhyme with "weiter" from the line above]

Statt Täglich hört man "Selenski, Waffenvertrag"

[I took some liberties on ^this line because it didn't quite make sense to me before. If you want to keep it closer to what you wrote but have it sound a bit better you can replace "Statt" with "Stattdessen gibt's" or "Stattdessen heißt's"]

Wann Als auf unserm Land war keine USA

[^this sentence structure is still wrong, the verb is supposed to be at the end, but if you correct it fully the rhyme doesn't work anymore, so i'll leave it half-right and call it artistic freedom or poetic license

Weil Denn die DDR war unser Staat --

[If you use "weil" you would have to invert the sentence structure and the rhyme would fail]

I'm not the best at writing poetry, i'm sure someone with more artistic inclination could find more elegant solutions, but this should be good enough.