From your official FAQ (now deleted and replaced, see update below) about the Code of Conduct revisions (I've bolded the parts that I find objectionable):
Q9: Do I have to use pronouns I’m unfamiliar or uncomfortable with (e.g., neopronouns like xe, zir, ne... )?
Yes, if those are stated by the individual.
It has long been a principle of American jurisprudence that the government cannot compel people to say anything that goes against their conscience. In the famous 1943 case West Virginia State Board of Education v. Barnette, involving parents who, for religious reasons, did not want their children forced to recite a pledge of allegiance to the United States, Justice Robert H. Jackson wrote:
If there is any fixed star in our constitutional constellation, it is that no official, high or petty, can prescribe what shall be orthodox in politics, nationalism, religion, or other matters of opinion or force citizens to confess by word or act their faith therein.
Now, Stack Exchange is a private company, not a part of the U.S. government, and the First Amendment to the U.S. Constitution is not binding on you. You have a legal right to create a Code of Conduct that compels people to use speech they find uncomfortable. This would be a violation of the First Amendment if a government entity did it, but you have the legal right to do it.
However, the fact that you are willing to compel speech that people find uncomfortable has persuaded me that you do not believe in freedom of expression. At least, not in this particular area of speech. And if you're willing to sacrifice that freedom in one area, you're going to be willing to sacrifice it in more areas soon, because you hold other things higher than freedom of expression.
I cannot in good conscience sign any Code of Conduct that compels people to speak in ways that would offend their conscience, or even that make them uncomfortable. My conscience is not offended by using the pronouns that people have requested, but I know that some people do find that their conscience would not allow them to use neopronouns. (I have talked to some such people). And since I cannot in good conscience sign your revised Code of Conduct, which you require all contributors to sign, the only principled thing to do is to stop contributing to your site other than this farewell message.
My only major contribution to your site has been in the f# tag, where I have a gold badge. As of yesterday, there were 12 gold badge holders in the f# tag, 4 of which have not contributed anything (questions or answers) for at least a year, leaving 8 active holders of a gold badge in the f# tag. Now that number has gone from 8 to 7.
P.S. It's one thing to say "Certain kinds of speech are not allowed on our site and will be removed if found". Everyone has to do that, since sadly, there are many people on the Internet who think nothing of trying to spam their advertising messages in places where such messages are completely inappropriate. The principle of free speech means that you must not compel me to be silent, but it in no way requires you to give me a platform if you find my message objectionable. But there's a big, bright line between "you do not have to give me a platform" and "you can compel me to speak in ways that make me uncomfortable or offend my conscience". You have blithely stepped over that line with no consideration of the principles of free expression that you are violating, and I refuse to continue to participate in a site that does not understand the fundamentals of freedom.
Edit: I do want to start a discussion about the principles of free expression, and the only place I've seen such a thing happen so far is in answers to other questions (such as this one or this one), where a discussion is harder because the only way to answer an answer is with a comment — and comments cannot be downvoted so it's hard to gauge how many people disagree with a comment, and more importantly it's hard to express a full idea in 600 characters when you're discussing fundamental philosophical/political principles such as free expression and what its limits, if any, should be. That is part of why I put "Coerced speech is incompatible with freedom" in my title: it's my reason for leaving SE, but it's also the subject around which I hope to spark a discussion. If this is a duplicate of other questions, I'd be perfectly happy to have this closed as a dupe, and have that discussion in the answers to those other, pre-existing question(s). But if this is not a duplicate of other questions, only of answers where a discussion is harder to have, I would respectfully ask that the question be reopened so that a discussion can be had in the answers here.
Edit 2: Thank you to those who voted to close this as a duplicate of a previous question, as I asked. But Aza's "An update on my resignation notice" post, while an excellent summary of many of the issues involved in this debate, does not touch on the issue that is at the core of this post of mine: the principles of free expression and how coerced speech is incompatible with freedom.
I would therefore, again, ask for this question to be either reopened, or closed with a duplicate that actually discusses the main issue I'm trying to address. I misunderstood the "This may be a duplicate" box that appeared at the top of my post to mean that the question had been closed. It has not; it's still open for answers if anyone wants to discuss the principles of coerced speech. Sorry about the mistake in my previous edit.
Update: The FAQ that I originally linked to has been closed and deleted, and replaced by a new official FAQ, which does not contain the specific language I objected to. I have not yet read it carefully enough to decide whether it allows the free expression I value, or whether it still restricts people from following their conscience. Until I have time to give it that careful reading, I will continue to stay off the site. (I did feel the need to edit this post to keep it up-to-date, which will unfortunately have the effect of bumping it back to the top of Meta.SE. So if any new comments or questions show up here, I will try to engage with them, but I will continue to refrain from commenting or answering elsewhere until/unless I make the decision to return. If there was a way to avoid bumping this up to the top of the active list, I would do so.)
Also, even if I decide that the updated FAQ sufficiently addresses my concern for free expression, I do not plan to return until Monica's concerns are fully addressed. The way Stack Exchange treated Monica was shameful, and nothing less than a full and complete apology and retraction (including unconditional reinstatement) is sufficient to fix the harm caused to her. (Requiring her to reapply for mod status is not sufficient, for the reasons Monica explained: when you fire someone without cause, it is a further violation to require them to come to you hat in hand begging for readmission. The only honorable thing to do is to unconditionally offer them their job back. Anything short of that would fail to acknowledge that you did wrong. Since Monica did nothing wrong, Stack Exchange must treat her as if she did nothing wrong, by restoring the privileges that were unjustly taken away from her.)