As a native German speaker, I was taught that the correct translation of "etwas gegen etwas tun", which would literally translate as "to do something against something", was "to do something ABOUT something", e.g. "You have to do something about this noise!". Since I keep reading "to do something against something", I'm now wondering if "do something against something" does not work at all, or if it would just be less common?
You're right, "against" (the literal translation of German gegen) can have this meaning in English:
against preposition (AS PROTECTION)
as a protection or defence from the bad effects of:
- We've insured the car against fire, theft, and accident.
- The police have to arm themselves against attack.
But this meaning is not idiomatic with all verbs or in all situations. The usage of gegen in German is more broad than against in English. You can fight against (some bad thing), you can protect against something, but in all these cases there's a clear sense of opposition, confrontation, defense, protection, etc. which comes both from the verb and from the preposition.
"Do" is a very generic verb, as in German (tun), and it doesn't really work with against. "Do something against the noise" is grammatical, but sounds very unnatural and is not at all idiomatic. "Do something about the noise" is indeed a much better translation.