Is "voelen zich" acceptable ipv "zijn"? "Ik voel me geirriteerd" was accepted on another exercise.
It's not really wrong, but a native speaker would never use that. Your sentence probably has the exact awkwardness same as the English equivalent: I feel irritated.
...which is used in another of the exercises! ;) So if it really is awkward, can the other sentence maybe be changed?
Must be due to that black lipstick...
This looks like a regular passive sentence, so why zijn instead of worden?
If you use worden, you are saying that they are being irritated by someone else, of if you take worden in the definition of becoming that they are becoming irritated.
I think there is some ambiguity in English here: passive present versus using a past participle as an adjective combined with "to be". Dutch does not have this ambiguity.
Can I say "Mijn ouders worden geirriteerd?"
Yes, when you know they will be irritated in the future