Although I have respect for and try to display courtesy to everyone as humans, and you do absolutely have equal respect from me as a human as do other humans of any gender, you are correct if you've noticed that I have more respect for A.P. than for you.
I normally try not to make a big deal out of whose writing and intellect I respect more and less, but since you're specifically asking for it I can't in good conscience decline to comment--if you have actually noticed the difference in behavior (and I'm not sure you have, honestly; you might be projecting based on nothing).
The reason is simple, and has nothing to do with sex.
Your arguments are simply not very well constructed most of the time. A.P.'s are. A lot of what you post--when it's not a one-liner, most of which are non-sequiturs in relation to the actual issue--I can guess the entire content of before reading. I can almost never guess what A.P. is going to say. You often display great reluctance to share your views when discussing views, making things sound like half a conversation, which makes things hard to follow and makes it hard to draw illuminating contrasts. A.P. shares views like mad--even if they're hypothetical views that A.P. doesn't even hold. After long discussions where I've countered basically all of your points, you end by making the same claim as at the beginning. With A.P. there's always progress. You tend towards single "gotcha" type evidence even in cases where things are complex and multifaceted; with A.P. there's more likely either a fundamental principle or a comprehensive study being offered.
You do sometimes ask interesting questions--half the time because they're good, half the time because they verbalize a common misconception that should be cleared up. And you have an oddly deep recall of at least parts of past discussions which can be enlightening.
But overall, reading A.P. is far more rewarding. It's difficult to be that engaging and well-reasoned (even if sometimes wrong), and that is something I respect.
So, yes, when it comes to writing on Medium, I admit--I respect A.P. more than I respect you, and if I have erred in the degree to which it has altered my responses (I think a little is permitted?) I apologize.
However, this is entirely 100% merit-based. If you like being more respected by people who like good arguments, your only option is to craft better arguments.
Just to give one prominent example of someone female--I think comparisons between people is rude so I don't want to overdo it--I have almost as much respect for Allison Gaines as for A.P. Gaines writes well, references heavily, constructs good solid arguments. I have a great deal of respect for her as a Medium writer, despite my exasperation with her occasional failure to check the content of references that are absolutely critical for her argument, and wishing that she would address more than one topic.
There are other female writers on Medium who I respect even more, but Gaines has the largest follower count so I've chosen her as the example. (Sorry, Allison, in the very unlikely event that you read this--I really don't think it's fair to critique people in public venues like this.)
Gender and sex have nothing to do with it. Most of the time I hardly even remember what sex (or race, or whatever) someone is. I care about the argument.
And when it comes to individual rights like bodily autonomy, I care about everyone--meaning everyone gets their rights, and nobody gets to step on anyone else. If a conflict is unavoidable--first try hard to make it so there isn't a conflict, then go for the least violation of rights you can manage (splitting the difference between minimax and lowest sum of violations).
I suppose it's possible that people who are not particularly inclined to abstract thinking cannot even conceive that someone could completely divorce identity from argument. But to someone who abstracts and generalizes very readily, the idea that what is relevant to the argument is anything but the argument is kind of peculiar--like, should it also matter if Venus is is Libra, or if it rained in Mali that day? If Paul is a man, and men are mammals, then Paul is a mammal, unless Biden held a press conference today, in which case Paul may well be a reptile?
Anyway.
In conclusion: more respect for A.P. as a Medium writer: yes. Has anything to do with gender: no.