The X-Card can be abused to push a plot you want – I recently had a discussion about this, with another person insisting on this being a use of the X-Card

"So, we're in setting XYZ, there are some women …"
Player holds up the X-Card. "No women please"
What?

– this isn't a problem of the X-Card, but of the players you're playing with. You didn't use extreme examples as this, but

The X-card doesn’t prevent bullying, it empowers it. It gives one person at the table the power – albeit only by social convention – to interrupt and spoil the fun of everyone else at the table, and to greatly inconvenience the Games Master.

sort of goes in that direction …

Your analogies are rather bad too …

Imagine you’re riding a roller coaster,

What do you expect from a roller coaster? Loopings, high speed, etc. - everyone knows that.
If you don't want that, don't go on the roller coaster.

You buy a ticket for a horror movie and enter the theatre.

What do you expect from a horror movie? Horror.
If you don't want that, don't watch the movie.

The Spawning Caves of the feral miscegenated Neo-Arachnid Variants

What do you expect from this? Spiders. Fair enough.
You shouldn't attend this with serious Arachnophobia.
_{(You flipped the "Expectation→Attending" here, breaking the analogy btw … Earlier: Thing A gives me B, I don't like B, but I check out A anyways. Oh, A is bad because of B! – Now: Thing A gives me B, let's not attend)}

Other scenario: You don't like spiders, and see my friendly face at a table at a convention, asking you if you're up for a DnD5e oneshot about dungeon delving.
Do you expect spiders? Not really.
But they're the third planned encounter.

You glossed over the most important use of the X-Card, not knowing how players you don't know (i.e. at conventions) tick.
Yeah, you may ask them "Is there anything you don't want to happen?" and they will most certainly answer "No", because they don't want to list hundred things they don't want.
I don't want to be punched in the face while playing RPGs, or I don't want to play 10 minutes to then hear "Rocks fall, you die", I don't want 2 hours of rules lawyering, I don't want my characters to be raped in a dungeon delving game, but I don't mention all these things, because I expect to be on the same page with everyone (not just the GM, mind you!).
In case these implied expectations don't meet up the X-Card comes in.
The alternative would be for me to leave, in case the GM (or another player) were to insist on punching me in the face/rocks fall you die/…

But even then, if you're new to RPGs, you don't even know what to expect from RPGs in general.

First session, GM asks: "Anything you're not good with?" "Nah" "Great"
20 Sessions later
GM kills a sick NPC the characters bonded with over the last 6 months.

One player in particular is hit very hard by this, because it reminded them of a death of a relative (unknown to the GM), they cry for 10 minutes and then leave, without saying a word afterwards.
Well … There being a simple way for the player to call for a time-out rather than having to speak up might have helped here, so the GM would skip the NPC's last minutes, to avoid the player leaving. Maybe not though, depends on the person.

If you have a regular group then you already know each other’s social, emotional and other boundaries and have negotiated them – probably – for years. In that context an X-card has no role whatsoever.

That is true, but I was still amazed, when I recently got to use the X-Card in a Cyberpunk setting Fiasco game, where I was a homosexual Joygirl, and a friend of mine was my pimp who was sexually interested in my character _{(because Cyberpunk and crazy fiasco characters, we all laughed at this idea, too)}
Then my friend got a turn and wanted to rape my character.

Me: "Please don't. I'm not in a mood for that. I want fun times, and not role play getting raped."
Friend: "Eh, okay, I can understand that."

That was an incognito X-Card. No feelings were hurt, no one was bullied. The game went on well, and we had drug fueled orgies (with NPCs) jumping from space stations _{(because cyberpunk, and crazy fiasco characters)}

There’s nothing there that can actually hurt you. It’s all words and numbers, descriptions and choice.

Yes, but why do you turn up for the game? To have fun.
If you're not having fun (or even having a horrible time), you shouldn't be playing. But if everyone agrees to skip/change the bad part for you, so we could go back to fun everything is fine again.

Thirdly, the idea of X-cards is part of a general trend to try and homogenise and beat down gaming into some sort of family-friendly, pablumesque milieu where anything irreverent, dangerous, challenging, sexual or violent – anything that could even potentially upset or offend someone is done away with.

Which is, again, a thing for conventions and people you are strangers with. You don't invite people for a DnD game which then is about rape and overly descriptive violence, unless you tell the players beforehand, so they know what to expect.
But even in a normal game; RPGs are a conversation. When conversing with strangers, I want to have a good time, but make everyone have a good time. Being bland, homogenized and not pushing anyone's buttons makes this easier.

The responsible thing to do, if you’re someone who has a hard time with certain plots, actions, monsters or whatever else at the table, is to remove yourself from the game at these points – or completely

That is a statement I would like to end with, too.
If you have a player abusing the X-Card/bullying with it:
You have a tool for that: X-Card the player abusing the X-Card! Talk with everyone about the abusing player. If everyone is on your side you should tell the abuser to leave (if they haven't left themselves already).
If you have a player using the X-Card, in a way that throws a wrench in your planning: X-Card the player this X-Card'ing the important plot-point!.
The X-Card itself means:

Can we skip/change this part please? I don't want this right now.

X-Card'ing the X-Card then means:

Timeout! Let's have a conversation about this, our expectations need to meet up, before we can continue playing.

If you're not having fun: Use the X-Card. If you're not having fun by someone (ab)using the X-Card: Use the X-Card. This applies to both being a GM and Player.
If you can't agree on a way to continue having fun someone needs to leave. That someone might be the X-Card-Player, the X-Card X-Card'ing-Player, or the GM.

Talk about it.

_{I hope this text-wall makes sense, I'm super tired}