>I guess my question is this: Is ignoring gender when interacting with co-workers wrong? Should I be doing something different when I interact with female co-workers?

Me being sexed female doesn't really qualify me to answer this question--I'm just some random person and have no formal power to speak as the official representative for Women Everywhere (I'd be a very bad choice for that, too--I am so masculine that I tend to be perceived as male, that's part of what I meant when I called myself a "living edge case" in my earlier comment).

That disclaimer out of the way, two points to your question:

1. It's highly unlikely that you are treating women identically to men, even though you genuinely believe you do. I'd bet hard money that you don't, actually, because a) almost nobody does, myself included despite my best efforts b) I can already name an instance where you didn't--you specifically asked me this question based on my sex and only my sex, by your own admission. I don't know how much you've read about unconscious bias, but it's a very well-studied and documented phenomenon and I recommend looking into some of the research on it that's been done. Hiring managers are more likely to extend offers to identical resumes that have male names, and the offers they extend to the male-named resumes tend to be higher. Startup pitches given by male actors are rated as more convincing and more likely to earn investment by VCs than the exact same pitches given by female actresses. Women are interrupted much more frequently than men in group discussions, and a group will perceive that women have talked "most of the time" if they talk for >=30% of the time. Men are perceived as more technically competent than women. Women are perceived negatively (too aggressive, "not a team player") for negotiating their salary, in general, whereas men are not. Even if you specifically are 100% egalitarian and have no mental shortcuts that you apply towards women whatsoever, the vast majority of the people they're interacting with are not truly gender blind. This is from people who really believe that they are unbiased, in a lot of cases, and aren't aware of the subconscious stereotyping that's driving their behavior--that's the unconscious part, and it's insidious. So, consciously saying "well I believe the genders are equal and I treat everyone the same and that's what we should do in the workplace, not take sex into account at all and just be buds" can just leave subtle sexism totally unchecked and rampant, instead of truly promoting equal behavior. Harvard hosts a couple free online tests to check your implicit bias, if you're curious to check yourself: https://implicit.harvard.edu/implicit/takeatest.html (I come off as biased on gender, for the record, most people do, regardless of their sex.)

2. I think this question, like affirmative action, comes down to whether you think it's more ethical to prioritize equality of opportunity or equality of outcome. Women in general are socialized to defer to the people around them, be more caring, be less assertive, be less confident. That has already happened by the time you're hiring them. If you and everyone in your workplace somehow do overcome your socialization and years of mental heuristics and manage to treat women in the field exactly the same as you do men in the field, the women will still have lower salaries (don't want to be confrontational and negotiate aggressively), apply to your job openings less (women do not apply to a job unless they meet the majority of the listed qualifications, unlike men), be less likely to voice their opinions in meetings, etc. Note here: I'm not saying all women act like this or every individual woman is more likely to than every individual man, I don't as far as I'm aware, but I'm saying that a random sampling of women are in general more likely to than a random sampling of men are. I'm sure you've seen that internet argument half a dozen times already, but in general the argument for treating everyone the exact same way is that you're treating everyone equally and that's the best you can do, even if there's disparate outcomes we shouldn't treat people differently, we should just control our behavior and make sure that's egalitarian. The argument against is along the lines of: we don't tell people confined to wheelchairs "the stairs are open to you too, stop fussing", we build ramps for them--the starting points for the two groups are not equal, therefore treating them the same isn't really egalitarian in the first place, it's just keeping the (unequal) status quo.

I can tell you that I personally would be extremely unhappy if my coworkers decided to behave in specific ways towards me because of my sex, but I'm, like I said, an edge case. And, on the contrary, I've had coworkers (correctly) guess that I am attracted to women and make awkward non-sequitor statements about their lesbian relative/friend and how happy they are for her--I actually am really pleased when this happens, even though it's always extremely awkward and we both know why they're bringing this up out of the blue. It lets me relax about it and just act normally without it affecting my career. (An aside: my first internship, my boss was big on listening to Rush Limbaugh in his cubicle, I wasn't working in a state where sexual orientation was a protected class, and I wasted a huge amount of mental energy agonizing over him potentially firing me over it, 0/10 internal conflict would not recommend.) So even an individual can have conflicting feelings about their minority status being explicitly accounted for by their coworkers, you can't really generalize.