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(Fair warning; my talk about Chrono Cross may not be perfect, because I am, 1: talking from memory, and 2: my memory is about things I read about the game when I heard about there being a sequel to the game I belove above basically all else. So it's possible that I may be misremembering some details leading to me stating something that is technically not true and that the game is less harsh than I remember it being. BUT, at least to my memory, the ways they got fucked over were rather extensive.)

Chrono Trigger implied that, with the defeat of Lavos:
Prometheus/Robo got to live in a 2300 AD that was not post-apocalyptic, with his robo-girlfriend very much still alive, and he himself was very much alive.

In Chrono Cross, they explicitly killed off Prometheus as part of the plot. And it is, explicitly by Word of God, him, Robo, the character you played from Chrono Trigger, you are killing. It's literally stated to be him explicitly by Word of God. (I believe the quote was something to the effect of, "I'm surprised players of the original game are not reacting more strongly to this death", in regards to Prometheus's mandatory destruction.) That's 1/7 player characters fucked over.

The Kingdom of Guardia is implied to last a long, long time, maybe to 1999 AD if not longer, and without Lavos may have even survived to 2300 AD.
Furthermore, Chrono and Nadia explicitly get married (this is admittedly shown in a cutscene that technically does tie the game to Chrono Cross butstill), and in the game it is explicitly stated they have descendants. They have children meaning they live decently long lives--and their children are still in positions of reasonable power, given that the descendant in 2300 AD was explicitly the head of his Dome.
Porre is shown to be prospering with a loving mayor that has a happy family and there is a boat fairing people from Porre to the kingdom of Guardia in peace that is stated to be expanding to Medina Village, with the implication of bringing in an even greater era of peace by the connection of the world.

Suffice to say: Dalton seeing Porre as the basis for his new empire, conquering the kingdom of guardia causing it to fall, with the explicit implication that , causing the entire kingdom to fall and for all of the above to be destroyed? Can't get more of a gut-punch than that, can you?

OH WAIT but you CAN by killing off Lucca in the plot of Chrono Cross! Which, when you add in the deaths of Chrono and Nadia and the destruction of their work and legacy, brings the player characters from the original game fucked over from 1 (Prometheus explicitly killed per Word of God) to 4 (Lucca killed in the plot, Prometheus killed in the plot, Chrono and Nadia in the background of the game).

And then to add insult to injury, Glenn's legacy was the powered up Masamune. He got it powered up by getting closure on Cyrus after having faced Janus. Well, the masamune ends up corrupted, fucking over Glenn's legacy, too! (Admittedly, I am aware that Dorean chastises the misbehaving Masa and Mune and that after doing so the blade becomes good again, bustill. It's an initial fuck over.)

Add to that that while Janus was planned to be in the game, but in the final version, wasn't? He ends up, technically, getting no closure and basically not existing, being absent. So while he wasn't fucked over the way the other 5 were, his absence means he's still honorarily fucked over.

Plus, the bonus boss saying "this is not your fight" when you can be max level and your characters are destined to, in the course of letting it be the next protagonists' fight, going to basically ALL END UP DEAD, in a game that explicitly has tones about not believing about destiny/fate in the first place for added bitterness, is just another gut-punch on top of the existing ones.

I think that Chrono Cross is a poor sequel, but is actually a good game if you pretend it is completely unrelated to Chrono Trigger

I actually played Chrono Cross first, and really enjoyed it.

Which then lead me to playing Chrono Trigger, and really enjoying it too.

So, basically, I think that Chrono Cross is a good game, but the "sequel" elements are poorly done.