Religious Rights clashing with Gender Equality

So I read a recent news story about a court ruling that college professor has the right to sue his university for reprimanding him. In that case, he refused to refer to a trans student by their correct gender in class (Mr/Ms) citing his religious views. This, along with the WV teacher post the other day, got me thinking about where we draw the legal line on the imposition of sincerely held religious beliefs on equal rights in a classroom, in this case gender rights.

Here is a scenario for debate.

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A professor has a religious belief that women should remain silent in class and does not allow them to speak in his class. In each first class session he puts up the bible quote that he feels supports his position on women remaining silent, he explains his stance, and tells the students that they can drop or transfer out of the class if they are unhappy with it. This same course is available with a different professor. After numerous complaints, and an investigation the university decides to terminate his employment. He decides to sue the University saying that they were discriminating against him for his religion, and infringed on his religious freedoms and first amendment rights.

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So, you're the judge ruling on whether the University is guilty. Who is in the right? Would it matter whether it's a public or private university?

*edited to add that the course is available with a different professor and reword my question.