Rammstein are definitely left-wing by their own admission. The song you’re referring to is called ‘Links, 2, 3, 4’—if you’re familiar with Bertholt Brecht, this is a direct allusion to the Einheitsfrontlied. Rammstein composed this song after frequent condemnation for being Nazis, owing to the band’s militaristic image as well as peculiarities such as the leader singer’s, Till Lindemann, rolling of Rs, which is often linked with Hitler’s oratory. The music video for the song is an allusion to countless ants (resembling the oppressed masses) uniting to destroy fascism/Nazism represented by large beetles. The lyrics state the following:

Sie wollen mein Herz am rechten Fleck doch, Seh’ ich dann nach unten weg/weck, Da schlägt es links.

They want my heart in the right place, but (double-meaning: right as in correct as well as right-wing, like in English) I then look down, It beats to the left (the heart is also beating towards the left of the political spectrum).

Rammstein’s band members all grew up in the GDR; however, as far as I’m aware, two of them have made pretty clear statements about their experience. Till Lindemann, in spite of his chaotic on-stage appearance, has lamented the loss of authenticity and retains strong connections to how life was in the East. His father, Werner Lindemann, was a poet and was awarded a prize for his contributions to socialist children’s literature.

Christian ‘Flake’ Lorenz is unapologetically pro-GDR. That’s not necessarily to say he is a perfervid socialist or communist; however, he is adamant in that he misses the GDR, and Lindemann stated: ‘Flake is still a citizen of the GDR, and he will die a citizen of the GDR.’ Flake is quoted as saying ‘free of trouble and pressure, we all had enough money to live.’ He even wrote an essay explaining how he misses the GDR, and he also is a vehement critic of the ‘decadent’ United States. Such feelings are undoubtedly reflected in the song you linked, Amerika. ‘We’re all living in Amerika: coca cola, sometimes war’ and ‘This is not a love song. I don’t sing my mother tongue’ are examples of discontent with American imperialistic and cultural hegemony.

The band members started out as punks during the final years of the GDR as well. There are interviews where Lindemann was vehemently clear about opposing Nazis, laughing at the assertion that he himself could be one. „Wir kommen aus dem Osten und sind als Sozialisten aufgewachsen. Wir waren früher entweder Punks oder Gruftis.“ Und er positioniert sich ganz klar mit der Aussage: „Wir hassen Nazis!“ (‘“We come from the East and grew up as socialists. We used to be either punks or goths.” And he clarifies his position with the statement: “We hate Nazis!”’) This goes to show that the band members never forgot their socialist education, even if most are apolitical now.

Undoubtedly they are socially liberal given their portrayal of Deutschland/Germania as a black woman in the song ‘Deutschland’ which induced a lot of right-wing tears, and the numerous times they’ve upset officials in Russia by mimicking homosexual acts while on stage. The song ‘Mann Gegen Mann’ is critical of homophobia and it’s music video is pretty outlandish.

Lol I just know Du Hast by them

It’s not music related but, iirc, Vigo Mortensen had an interview at the height of his Lord of the Rings fame. He said something mildly communist and was never really interviewed again on mainstream TV shows. (Looks like he spent some of his childhood in Argentina, btw.)