Generally speaking, humans - even professors with a bad reputation - behave the way they do in a way that is sensible in at least some context, even if that context is only in their own mind. Without knowing the situation, this behavior could be anywhere from an indefensible prejudice to a "reasonable person" response that one simply fails to understand or have sufficient information to interpret.
So, let's walk through a couple of reasonable interpretations.
In the first interpretation, the professor responded honestly - she felt fear or discomfort in meeting with you privately. "Why" she felt that way cannot be determined from a simple reading of the narrative presented. She could have a disability (panic/anxiety disorder, post traumatic stress), she could have been threatened in the past, she could have believed you were affiliated with people who had threatened her or wished her ill, or she could have interpreted your tone or body language as being angry or...well, intimidating, and surely other reasons I cannot so easily imagine.
People have a right to feel safe, and to insist they not be put in a position where they are made to be in perceived or real danger. When one can un-self-consciously walk down a dark street alone without fear because of one's skin color, size, gender, or physical training, it is easy to be unaware of the fear that others who are not so fortunate must live in continually - often for all too real reasons. As I have two daughters, I can attest that this is a rather disgusting realization to have to come to - but it is an important one in understanding our place in the world and our relationships to others.
Legally and ethically, the University is almost universally required to provide reasonable accommodations to this end for both students and faculty - both you and your professor.
In all this, this does not require that you did anything wrong, nor that you should receive adverse treatment. If the professor was hard of hearing she could require all advisement to be by email, and this would be a reasonable accommodation. To request an appointment with a chaperon might feel silly when you don't see the need, but it can be a reasonable accommodation none the less.
Unfair Treatment Interpretation
Interpretation Two: you were singled out for unfair treatment. In this interpretation, you were treated explicitly unfairly and the professors attitude and actions culminated in adverse, unwarranted treatment.
As a student and "paying customer", you have the right to receive services you paid for, comparably valued substitute services, or a refund. The University makes certain guarantees of service, and they are obligated to make good on their contract.
The University, along with applicable law, usually provides for how complaints should be handled. Generally, the head/chair of the department is involved, and at times special departments (like an Ombudsman or Student Services) can also seek to find a reasonable resolution.
There is not, however, always a guarantee that a class will be offered by a professor who likes you, or whom you like, or who is even in any way helpful or beyond vaguely useful. It's hard to bar passive-aggressive behavior that's shielded by unethical but hard to disprove veils of personal boundaries or safety.
From your writing, it seems a member of administration offered a number of remedies. You likely had the right to complain to administration, be given an administrative (no cost/fault) withdrawal from the class with potential return of related fees, receive 3rd party grading to remove questions of improper marks, a pass/fail opportunity for credit, etc. While none of these are ideal resolutions, there are often no perfect fixes for problems like this.
Part of this is often what is really sought in remedy is not possible or not stated. If you felt insulted and discriminated against, you might have wanted the professor penalized or to apologize to you - which might have been objectively inappropriate or just impossible. You might have wanted your paper regraded as stated, but there may have been insufficient grounds for this is as it is simply an extraordinary request. If a 3rd party can look at your paper and say "it is not beyond reason that a professor, even if they would be very harsh, would have given this paper a C" then it's just a no go there, too.
So, administration has a duty to find a way to make the best of a bad situation. From the sounds of it, they offered pretty much all the recourse they had to offer to you. You could take it or leave it, but by staying in the class and taking the pass/fail offer and receiving credit (and choosing not to attend lecture - which was certainly understandable but not strictly demanded by the situation) the University upheld their end of the bargain - albeit in a not very satisfying way.
A Word on Feminism
One note of issue: the problem with how this is stated in the post is that feminism isn't actually related. If someone is known to have a militant or unkind attitude, behave in a way that discriminates against certain genders or types of people, or just has a reputation for being a terrible teacher or nasty person, say so.
The problem is when words are used as code words for something else entirely. If the administration was unwilling to give a refund it would be appropriate to say they were playing hard ball or being stingy or greedy - not to say they were known to be of a certain ethnicity renowned for thrift (to be time-insensitive, I am presently aware of three entirely different sets of people who have this notion assigned to them).
So, if a professor has a reputation of being nasty or terrible or discriminatory, please just say so outright. To say "feminist" or "extreme feminist" to imply being a man-hating shrew does a dis-service to yourself, your question, to feminists, to man-hating shrews, and to society as a whole.