…I think that, though most focus on the 2.5 children part, that is not the core problem people have with the epilogue (at least afaik).
The books were about love and family, true, but they were also about change - the more we learned about the wizarding society, the more it was obvious something would have to happen to it for a truly happy ending.
The prejudice (of muggleborns, of creatures, of muggles) was, in the earlier books, mostly expoused by Draco and the other Slytherins - and once later books came out we saw that it wasn’t just entrenched in society itself (which we can deduce mostly from the sheer number of Death Eaters) but in its government, which clashes with Harry in the form of Umbridge.
Thus we see that the government as it was (bumbling Fudge, who agreed to send Hagrid to prison and was going to give Sirius the Kiss, Fudge again who refused to listen or even believe that Voldemort had returned for a second, the whole wizengamot who was going to condemn Harry for flimsy charges, Umbridge who saw enemies of the ministry even in children and treated them as that, even Scrimgeour who wanted to use Harry for his own means) was an enemy, was what our protagonists were going to go against.
(And once Voldemort takes over it, they can go against it AND him at once quite neatly.)
One could argue that the house system itself was a generator of prejudice (”Hufflepuffs are all duffers, Slytherin all go bad”) - and tbh whatever bad things many Slytherins have done, it is still no reason to treat newly-sorted eleven year olds like potential enemies. (A passage that always gets me is the twins harassing some poor first year Slytherin who has just been sorted on his way to the table - it’s never addressed, not even given an explanation.)
If the series had ended with the main battle won, and the heroes just looking out with hope towards the future (as the chapter before the epilogue closes with), I think few would have had issues with it. One could even suggest a family in the future for Harry, with him and Ginny reconciling after the whole ordeal.
It’s not the family itself that is the problem.
It’s the repetition - or rather, the continuation - of all the things that led to the chaos and pain of the wars in the past. Things that we were promised would change thanks to our protagonists, but which are just reinforced.
We learn Ron has Confunded the hapless Muggle testing his driving, and the two derive mirth from it (thus showing not an ounce of respect towards a fellow human being, and continuing the trend of wizards being better than Death Eaters because they do not kill Muggles, and then turning around and treating them like witless children to be manipulated, as shown during the Quidditch World Cup from how the owners of that camping site were Obliviated so repeatedly that they were losing their minds, or when Harry’s actions on his aunt were brushed away quite easily, or when Hagrid cast magic likely to be permanent on Dudley, who had to have his tail surgically removed).
We hear Ron reinforce the Weasley-Malfoy feud, through the proxy of their own children.
We learn that Draco has had pretty much no contact whatsoever with them, and that there is still tension despite the 19 years that have passed.
We hear Albus Severus scared that he would end up in Slytherin, and Harry consoling him by telling them that Slytherin can be brave too, and that in any case he can choose not to be in that house (and how comes he never heard of the “war hero Snape”, unless the image of Slytherin is still that of the evil house, Voldemort’s house).
…And sure, these aren’t the same as “Muggleborn registration” or “terrorist attacks on Muggles”, and it IS still kind of a happy ending by virtue of that not being there.
But the cracks are plain - there has been no actual deep change in the wizarding world, just a soft reset. And from that soft reset, another Dark Lord can rise again - and likely will.
I do think that most readers not identifying at all with the dream of a picket fence family helped the negative reception. Tbh it feels also like a generational thing - most people grew up alongside Harry Potter, and strongly identified with its themes of rebellion… And then he grows up and becomes the embodiment of the unrealistic dream of their parents’ generation. THAT sure wouldn’t sit well with most.
But the insidiousness of the epilogue is that it is that, coupled with the cracks under a peaceful facade - and, given the surface is already something many dislike, the aforementioned cracks (which, I grant, are tiny and could be easily explained away) show all the more and end up under close scrutiny.
Harry Potter was a very rebellious story, as I mentioned - the protagonist is first hounded by the (at the time legitimate) government, sees its corruption and flaws, and then fights against it.
To see that rebelliousness turned dormant without a clear resolution to it (as in, a significant change in the attitudes towards muggles, muggleborns and creatures, as well as perhaps a complete overhauling of the house system or it not mattering as much, since - as the Hat even said! - they are stronger together and shouldn’t be so divided…) turned many people sour, me included.
If the family had come alongside that societal change, then more power to Harry. But it almost looks like the trio turned a blind eye to the deeper issues and just… gave up.
(Also I am loathe to talk about the Cursed Child, but that Albus was treated so badly once in Slytherin, that Scorpius had his family maligned and a connection to Voldemort hanging over his head, and that Delphini so easily moved forces - and that Harry and Hermione would be so ineffective as to let them gather - shows that yep, society hasn’t actually changed at all and the whole thing will explode again as soon as enough fuel gathers.)