March 11, 2023.
This review contains spoilers for seasons 1-6.
Taylor Mason, a non-binary main character, very much breaks the mould of an otherwise typical drama show, and is played by a non-binary actor named Asia Kate Dillon. Initially they are an anti-social stereotype of super-intelligence, but develop an actual personality throughout later episodes, and have romantic relationships with both men and women.

Lauren, Taylor's employee, about to kiss them for the first time in episode S04E09.
Their adversaries, even when plotting how to take them down, continue to use their correct pronouns. The consensus is generally that Taylor’s business practices and dealings are fair game to criticise, but their gender is not. I really enjoy that aspect of the show, and the fact that Taylor is portrayed as a clever, capable person who isn't afraid of conflict.

Taylor, moved to tears after their father makes an effort to be accepting in S04E03.
They are misgendered a few times by antagonistic and ignorant characters, and also by their father, who is struggling to affirm his child's gender. The misgendering gets less and less common throughout the series, and with every season Taylor's gender is less of a topic to be actively discussed. Billions is probably the most long-running show which normalises gender-neutral pronouns in everyday use.

Taylor Mason wearing a wig, makeup, and a dress.
In S04E01, in order to secure a business deal with a Arabian sheikh who has anti-LGBT views, Taylor presents femininely and goes toe-to-toe with a representative who insists that "females" ought to play submissive roles in business, and in life overall. This is an example of Taylor's ruthlessness, and the extent to which they sacrifice comfort for business and victory. They're not particularly emotional or vulnerable when it comes to their gender or the pronouns used to refer to them. Unless the person misgendering them is their father, they react with calculated words or just ignore the comments entirely. I like that aspect of Taylor's characterisation. They're very self-assured and calm. Any issues they face relate to other parts of their life (work, relationships, etc) and not their gender.

A watch that Taylor buys in S03E04, which costs $164,400.
The show is ongoing and Taylor remains an influential main character. But there’s no escaping the fact that Billions' central themes include capitalist corruption and rich people’s drama. Taylor themself plays "the good millionaire" in later seasons, which– given the current dialogue about wealth inequality in America– may dissuade some people from watching for the non-binary representation. The antics of the mega-wealthy do get a bit ridiculous after a while.

A woman who is used as a prop in S01E02.
The worst aspect of the show is its misogyny, including the tokenising and manipulation of a female rape survivor named Martina Slovis. Season 1 kicks things off with nameless women in a prostituting massage parlour and a nameless dwarven woman offering sexual services in a bathhouse, so that should give you an idea of the show’s standards when it comes to women and minorities.
The afore-mentioned short-statured woman walks up to a main character and undresses, as pictured above. She is never shown again, relegated to just being a fetish. Entertainment Weekly wrote, "Hall is seen siting in a sauna when, out of nowhere, a dwarf comes up to him and disrobes. Billions! I get the feeling we’re going to learn everyone’s sexual proclivities by the end of the season." The woman, like many other women in Billions, is nothing more than an object. We don't even see her face. She has no name. She's just "a dwarf" and therein a "sexual proclivity".
Even in later seasons, when the show is apparently more progressive, the m-word is used by a character recommending dwarf-tossing as an activity to boost office morale. This is a reference to The Wolf of Wall Street that's pretty tasteless, considering modern awareness of the damage such a practice causes, and the dignity that short-statured people are clawing back from a culture that has ridiculed and abused them.
A cis gay character also jokes about a colleague supposedly having a vagina, meaning he's a weak and pathetic man. So yes, there's a non-binary main character, but there's also anti-FTM transphobia. Hearing the throwaway comment, I couldn't help but think of Carter Brown’s experiences. Of his colleagues, Brown recalled in this interview, “They confronted me and said that it had been rumoured that I was a woman. Or, better yet, that I had a vagina.” A lot of violence, especially sexual violence, occurs to trans men when people make such comments. So a joke about a man having a vagina hardly signals an FTM-friendly show, for FTM viewers who have been the target of such comments.

"She's an illegal just over from El Salvador."
I would advise reading reviews before you dive in, especially considering racist storylines in recent seasons, one of which involves Taylor directly. They force a man of colour (Leon) out of business because he refuses to have his money invested with the police. In season three, a woman named Maria Gonzalez is forcibly detained and deported by ICE, in order to cover up the white protagonist's crimes. There is also a poorly-handled, graphically-described storyline about police brutality against a man of colour (Jose Lugo), which ultimately serves as little more than an arc to explore a white dude's professional trajectory.
The same white dude (Chuck Rhoades) also seeks the help of black market organ harvesters, whose primary suppliers include vulnerable refugees and minorities, to help his obscenely wealthy dad get a kidney transplant. He ultimately doesn't go through with the transaction, but also doesn't use his power as a literal law-enforcer to get the black market surgeon thrown in prison. In fact, the predatory surgeon hangs around for... comedy relief.
Pretty much every main character is morally bankrupt. Taylor is an example of good non-binary representation in the sense that they're played by a non-binary actor and allowed a personality beyond their gender, but they're not a very good person. I'm glad that this is the case, actually, and that the show treats Taylor the same way it treats cishet characters. Every human being can be corrupted by wealth and temptation, after all, and gender-diverse people aren't all perfect. If Taylor had been a morally incorruptible, idealised person with no flaws, they would've been ridiculously out of place among the other characters. If they were going to have a place in this show, amongst awful and selfish people, it makes sense that they're periodically awful and selfish too. That doesn't stop them being non-binary.

Chuck and his father in S03E04.
One of the creepiest aspects of this show, in my opinion, is the relationship between Chuck (a main character) and his abusive father. At 14 years old, his father and uncle hired an adult female "prostitute" to have sex with him and, as an adult, Chuck's father kissed his son full on the mouth and held him still even as Chuck tried to resist him. Not only did Chuck's wife react with mere mild surprise at her husband's description of statutory rape, the show does not treat his experiences seriously. It's a repugnant storyline that almost kept me from watching, especially when you consider how a character might react if a 14 year-old girl had been forced into sex by her father and uncle. The double standard is disgusting.
I'm increasingly infuriated by mainstream media treating male abuse as trivial or, at worst, comedic. This show does both, with Wags (a main character) asserting that he'd hire an adult female sex worker for a 13 year-old boy's birthday party, so the child could have his first sexual experience. I don't find this funny. I find it deeply disturbing.
Chuck's father, Charles, also uses ableist language and is generally an awful human being. He uses the r-slur in season 3, along with the phrase "physical moron", and degrades his brother-in-law on the basis that the man has microcephaly. He also calls Native American people "Indians". You're supposed to dislike him to an extent, but mainly, the writers seem to encourage viewers to laugh at his cruelty and racism/sexism/ableism/etc. It's rarely challenged in any meaningful way.

Ari Spyros leering at Bonnie, the target of his unrequited, sleazy advances in S04E09.
Martina Slovis' rapist (Ari Spyros) remains an established side character, the seriousness of his crime undermined by the fact that he's treated as little more than an annoyance by the main characters. Beyond the rape (which is quickly brushed off by the writers), Spyros is given free reign to freshly sexually harass women with no repercussions, supposedly powerful female characters like Wendy Rhodes having meetings with female colleagues about how to manage Spyros, rather than just firing the creep outright.
If you want to watch Billions, you'll need to make your peace with the fact that a rapist is inexplicably allowed to grope and harass his way through workplaces which are supposedly all-powerful and fully capable of sending him packing. At one point, Bonnie (a female employee) seeks Wendy's help after Spyros and multiple other male employees have subjected her to inappropriate attention. In response, Wendy smiles placidly like there's nothing she or Bonnie can do except manage these adult colleagues as though they're just silly, misguided children. As I watched, I felt like screaming! How about showing them the door and making the seriousness of sexual harassment known? Aren't you influential people who can demand better, for fuck's sake? Isn't Wendy, particularly, supposed to be the all-powerful woman of the show? The same woman who held up a bottle of Viagra during a speech in which she psychologically dominated a room full of misogynistic cis men? The contradiction is exhausting.
In summary: Taylor Mason is compelling and Billions is far from perfect, although I did enjoy it enough to marathon all available episodes. Most of the acting, especially Paul Giamatti's performance as Chuck, is superb. Just prepare yourself for a whole host of nasty people and loose morals.
You're supposed to hate many of the characters in this show, which is much of the defence behind actions/beliefs that the writers never bother to properly challenge. You're supposed to look at the power imbalances that exist between the main characters and other people, in terms of financial security and ethnicity and all aspects of life, and reflect on how closely those imbalances match real life. But that justification doesn't mean the show is always easy to watch.
Season 7 Update:
I'm partway through the last season of Billions at the time of writing. In terms of the show's non-binary representation, Taylor remains largely the same, although they and other characters have become cardboard cutouts of previously fleshed-out personalities. Taylor seems to be utterly vacuous, with no opinions about reuniting with the man who caused permanent loss and conflict in their family. They've been reduced to snappy one-liners and boring dialogue. Any compelling storytelling has gone down the drain, even beyond Taylor.
Episode 3 features body shaming via small dick jokes. Lazy, misandristic, predictable, shallow crap that's permitted by mainstream media as long as it's exclusively directed at men. Bleagh.