If there is required an article "a", then Romanian sentence should be "Soacra mea este o bibliotecară".
good question - Ive seen other duolingo accepted examples where the translation is something like "he is physicist"
it seems like there are some mistakes in this course, and this is understandable as it is for free
Most European languages omit an indefinite article before a profession, Romanian is likely the same. Careful before you label something a mistake.