Can the sex (ie. chromosomes) of a person or animal still be binary, male or female? Or is this not politically correct now too?

It is considered politically incorrect to bring this up, yes - but if a queer theory advocate chooses to engage with the debate, they will usually counter by bringing up intersex conditions and/or saying that the division of sexes by chromosomes is nothing more than a social construct.

Am I correct in thinking that "gender" now refers to "gender identity" which may mean whatever anyone wants it to mean?

It really depends on who you're conversing with, but yeah this is the safest assumption.

If a person's gender is not binary (male/female), then why still use the terms "masculine" and "feminine" to describe people? Doesn't that verify the reality of a binary nature?

I think they view gender as a continuum, and assume that people who are/identify as men and women exist at either terminal of that range. I can't quite figure out whether they see masculinity and femininity as social constructs or as endemic traits and I don't think they know either.

If a person's gender is not binary (male/female), then why are there even feminists? Shouldn't they all be humanists?

2nd-wave feminists, material feminists and radical feminists agree with you. Feminists who embrace queer theory would say, I think, that we still need feminism because women (including trans women, in their philosophy) are not oppressed so much on the basis of sex as they are on the basis of which gender society perceives them to be (the assumption being that society sees trans women as women). A lot of people mistakenly believe that wokeness operates on oppression points. This may be have been true in the past but now it's more like oppression + transgression of societal norms, with transgression being far more important.

Can I sexually identify as a Black lesbian dwarf yet look like and behave as a cis white male?

No, you are only allowed to identify as one of those things (lesbian). You will be vilified and ridiculed for identifying as either of the other two, no matter how much you change your appearance and behavior. Critical theory holds that the categories of man and woman have no material basis and are instead defined by gender, which is subjective, but also recognizes race and disability as material realities.

Can I consider myself "MehBisexual"? Now there's this "SuperStraight" thing that I don't get yet, nor really care. I was only bi for about 10 horny years of my life, willing to stoop to doing fat chicks or dudes against my preference for excellent specimens of women. Eventually I quit stooping because it wasn't worth it, and it wasn't fair to them, nor myself. I'm not ashamed, nor have pride, nor feel super - I'm just meh about it.

I don't know. It sounds like you weren't attracted to them, so I'd guess no, probably not bisexual. Did their bodies turn you on or was it really just a case of libido + opportunity? Do you fantasize about men and/or could you see yourself hooking up with them again in the future? No need to answer these here, of course - they're meant to be self-reflection questions.

I don't even know which gender sub to post this to, so my default is /s/Sex

I think this would have generated interesting responses in s/GenderCritical and s/GCdebatesQT. s/Sex makes perfect sense too but apparently no one was participating at the time.