I've heard this said, but there is no real evidence of it. Historically "his" has been used when the gender is not known (or more recently, "his or her") Common informal usage may be "their," but this is not considered proper grammar and would not be used in a buisness or academic setting.
I did some searching and opinions seem to be all over the place. It seems that (especially US) colloquial use is "their", the very formal use is singular, and there is a wide range in between. Some comprehensive and balanced views: https://www.uwgb.edu/writingcenter/handbook/TheirHisHer.htm
Again, common usage may be "their," but formal usage would be "he or she" or (historically) simply "he." I don't think anyone, no matter how politically correct, would consider "he or she" to be sexist. And again, I mostly take issue with the claim that "their" as a singular pronoun was some common historical usage. I certainly have not found that to be the case.
Teachers and students are of course more conservative than native speakers in general, we have to be - to learn what is idiomatically correct. But as a 'linguist' I am much more interested in the evolution of languages and comparing different languages. E.g. when I have to translate "le sue aventure" my first choice is always 'HER adventures', even though HIS is just as valid for an Italian. The roman languages (french, spanish, italian) have this choice every day, not feeling any difference, there is no 'stressing' if it is His or Her. But in English, Danish, Norwegian, Swedish, we don't divide words into masculin/feminine, so when we say 'His' or 'Her' it has the possibility to get a political stress, which wasn't intended. In Sweden people are at the moment trying to implement a new special word to be used as not to stress either sex (masculine/feminine). That's how far this evolution can get ... there are actually languages (e.g. Finnish) that has no word for 'he' or 'she', they only use 'it'.
But the sentence clearly says "ognuna" so it is already known that each one is female. There's no way that can be considered sexist and using the words "their own cake" is just wrong in this case.