Personally, Im not on the antifantasy side for either Higurashi or Umineko, since the evidence for hard 100% antifantasy in either stories is lacking.
To me both were written with a mix. That it was not all fantasy/spiritual/magical things, but also not all just physical things. Umineko demonstrates this much better than Higurashi - I see Higurashi as a kind of prototype story idea to the themes explored more in Umineko. So a strict division between the two can’t be as easily defined/cut in Higurashi as in Umineko.
That being said - I feel the antifantasy view lies in Takano. She held it throughout the story and until her end - she never wavered in her beliefs: that there is no Oyashiro sama deity, there is no curse - no spiritual miko or reincarnations - its just a small village with a bloody past caused by parasites. That the “deity” was made up for control. And she will proove that - and become Oyashiro sama in the process, showing that there never was an Oyashiro sama deity and it was all the work of human hand out of fear and control of this disease.
It can be said the scene where she saw Hanyuu in the shrine as the shrine deity could also be explained as simply Takano declaring her self as becoming the kami of Furude Jinja - something that isnt divorced from reality as say for example the time worlds. (Human beings are enshrined after they pass or for a great legacy they made, Takano’s research being the legacy) and in that sense become a “true” kami than the “made up” kami that was presently Oyashiro sama.
We know the 3 Great Houses had nothing to do with most of the Oyashiro sama murders (in the main story itself), but that also they werent afraid to get their hands bloody in some cases. So it is entirely possible they could have also manipulated, pulled strings, or had a hand in controlling the village with fear and knowledge of the virus. Mostly on their side to keep people from leaving the village and keep the village in tact. And to keep the integrety of Oyashiro sama despite knowing it is a made up kami and simply a virus( on the view of antifantasy here) whereas Takano wants to expose this and will carry out “curses” to do so more obviously.
The killings themselves can be explained by the virus, or perhaps the 3 Great Houses, at least the first few such as the dismemberment and then Satoko’s parents. The following we know were Takano, such as Rika’s parents.
But that leaves us to Rika’s prophecies. This is where a true antifantasy in Higurashi cant be fully achieved (whereas in contrast to Umineko, a full antifantasy can be interpreted/achieved in a sense )
She couldnt have known from the 3 Great Houses about the later deaths since we know especially Takano ordered the death of Rika’s parents as they got in the way of her research on the Hinamizawa syndrome. (And that death in particular goes against the houses ideals - why also would Oyashiro sama curse their own bloodline and descendants? It doesnt look good on the 3 Great Houses nor does them any favors. But it did for Takano)
Rikas prophecies, why she tells Akasaka, and her actions are all explained by her pasts in the old timelines /connections to Hanyuu and so on. These reasons are more spiritual/fantasy so they cannot fit in the antifantasy world.
But as we know most often dismissed her prophecies as childs rambling/the influence of growing up in the family of priests of Oyashiro sama (talking about curses and prophecies all the time - influencing a young Rika to act more mature or spiritual than she really is )
As we know as well, her prophecies can change quickly and are fragile when willed to change, and arent set in stone. Theyre not readings of a destiny, but of repeated events she had lived through and had knowledge of. We saw this how Keiichi easily broke all of her “prophecies” such as with the shop games. Keiichi’s attitude towards her there is a key to viewing her prophecies from an antifantasy viewpoint.
But again I dont really feel Higurashi can be 100% antifantasy so Im just referring back to some parts I can try to figure out a way to explain those difficult aspects - by how the other characters reacted to them.
In a completely antifantasy world, it would probably end as it did in Minagoroshi hen. To me that was the ultimate antifantasy world. Where no matter what faith they had or things they did, Takanos cold hard strong will, beliefs, and knowledge destroyed everything they worked for and built up. She won that world, and since she was on antifantasy view point, to me that is the antifantasy world. If there was no other timelines and just that one, Higurashi could be either interpretation 100% like Umineko can be interpreted (though personally I dont agree with that interpretations because of certain areas, but thats for another topic!) , but given the other timelines and events that give us more information/insight to the world, its not really possible 100% in my viewpoint.
(Perhaps that is why Bernkastel said there is no such thing as a real miracle. Even if its just 0.001% chance, a miracle can occur. But if it was a cold 100% certain world with no room for any other hope, a miracle in the sense of Bernkastels view couldnt occur. And in that sense it wasnt really a miracle, just reaching that incredibly low possibility…perhaps) 
(I also hope this made some sense ;; there is so much to think about but I didnt want to get too long so I tried to summarize as best I could, but Im happy to clarify/talk about the points more!)