Reading the PDF and using the search function is very handy. 3 comments on BY doesn't take a lot of effort to analyze. I was surprised there were so few comments.

A harder piece of analysis would be to look at Quirrell's views on gender. Harder to search on.

But the SPHEW protests provide some interesting tidbits. First of all, that Quirrell is there at all. Of the faculty, it's predominantly the female faculty, and Quirrell doesn't seem your prototypical human rights protester. He even had a button.

“You mean that’s how men would treat us if we didn’t have wands to defend ourselves?”

There was a short, sardonic laugh from the direction of Professor Quirrell. When Hermione turned her head to look she saw that the Defense Professor was still idly toying with the button, not bothering to glance up at the rest of them, as he said, “Such is human nature, Miss Clearwater. Rest assured that you would be no kinder, if witches had wands and men lacked them.”
“I hardly think so!” snapped Professor Sinistra.
A cold chuckle. “I suspect it happens more often than any dare suggest, in the proudest pureblood families. Some lonely witch spies a handsome Muggle; and thinks how very easy it would be, to slip the man a love potion, and by him be adored alone and utterly. And since she knows he can offer her no resistance, why, it is only natural for her to take from him whatever she pleases—”

Maybe Quirrell speaks with some authority about what women with power would do. EY has a habit of having his characters smile or laugh to themselves when they're think thing they're not entirely sharing with others.

“Professor Quirrell was testing Hermione to see if he wanted to be her mysterious old wizard,”

So that Quirrell took Hermione seriously in ways that others didn't. He also awarded her "100 points for doing what's right". And he tried to get her out of Hogwarts before she died. He looks to be another character who values Hermione more than EY's "feminist" detractors.