I have edited around that pronoun construction many a time. There is nearly always an alternative. One is to look for a phrasing with the relative pronoun “who.” For example:
If someone wants to ~~~, they {he or she} can ~~~
can be rewritten as
Someone who wants to ~~~ can ~~~
You can use the plural too, of course:
People who want to ~~~ can ~~~.
I have edited entire books for publishers who insisted on gender neutrality, not even settling for a balance of he’s and she’s. One of those was a counseling textbook that contained numerous passages pertaining to one (gender-neutral) therapist and one (gender-neutral) client, where I couldn’t even dodge behind the plural. It was a challenge, but I solved every instance. So I know it can be done. You just have to use different sentence constructions. I’d rather do that, myself, than just capitulate or leave myself open to a charge of incorrect grammar.
As for the passive, I champion and defend it as a perfectly legitimate and valuable English construction. It can be overused and misused, to be sure, but there are also times and places when it is exactly the right solution.
However, I have lately run into a number of instances where the critic was totally misidentifying the passive, having it hopelessly confused with any form of the verb “to be.” In one case, an author was criticized for overuse of the passive in a short story written in the past tense. The critic had circled every instance of “was”! They were all simple past tense. Only two occurrences in the entire story were actually passive: “was born” and “was adopted.” Definitely the right time to use passive. I would first be sure that this professor was accurately identifying the passive voice before looking for workarounds.
If you have made appropriate and justifiable use of the passive voice and yet the professor objects (and you can’t cite statistics to show you haven’t overused it), I would recommend malicious compliance: give her the active voice in every single instance and see how she likes it.