"My parents were workers."
Translation:Mes parents étaient ouvriers.
"Workers" being derived from "work", it is not always easy to determine what is meant: manual workers would make the sentence clearer to mean "ouvriers".
Other ways to refer to workers can be "employés, travailleurs, salariés" depending on context.
As to the tense, "were" can indeed translate to "étaient" or "ont été", the latter in passé composé suggesting that they did not spend their whole career as workers, while the imperfect is not precise on the duration, just on the fact that they are no longer workers.
Let's assume that if the speaker had two mothers, "mes parentes" would be used, and then "ouvrières" would work.
um no, workers = travailleurs, ouvriers = labourers, if you wish to be pedantic... all four can be used for the same thing though.