I feel he is probably like most Japanese people. religion in Japan and religion in Western societies are actually two different kinds of nuances. What we would call religion in the West is more spirituality or faith in Japan. Religion in itself is a more negative term, more like alluding to people bound to dogma. Kind of like overzealous people image.
Because of this, people dont generally like to say they are religious; but definitely most are spiritual or have some sort of faith in a higher power or the divinity of the natural world. That being said it is also entirely possible Ryukishi is atheist or agnostic. It’s unclear but also Im not going to make assumptions.
That being said, Ryukishi has a lot of Shinto themes in WTC, but especially Higurashi. (Higurashi full spoilers) Hanyuus sacrifice seems Christian but it is actually very Shinto. There are numerous once-human kamis (divine spirits) that had sacrificed themselves, whether in war or to keep peace, or even to clear away tsumi (which is translated as sin but is very different than sin) and are now enshrined as deities.
Tsumi is not sin in the Western sense but it is basically an “offense against the order of things” than specficially a sin which is considered something inherently evil or bad. Tsumi is very much the nuance of doing something wrong or offensive to nature or kami, or society (defined as amatsu/heavenly tsumi, kunitsu/earthly tsumi, and so on) but not evil or bad - if that makes sense. Even kami can commit tsumi.
The kanji for tsumi (罪) actually denoted a crime of some sort - but not that the action was inherently sinful, bad, evil, or malignant. Just that the tsumi was an offense or broke the order of things, or broke a social taboo. Generally we can understand most tsumi as bad or evil actions, but some tsumi is not, for example, knocking over a sacred item by accident. Or building a washroom without asking a kami’s permission.
When Hanyuu said they would clear the tsumi via sacrifice, this was kind of like a ritualized form of seppuku. And indeed even in seppuku, it became very connected to Shinto. The tray their innards are let out into is called sanbo, and this tray are only used for offering things to kami. It is said blood and so on is kegare (negative energy things) but since the whole ceremony was ritualized and purified with oharae (positive/cleansing energy) it negated the kegare.
In a sense that action was like Hanyuu clearing the tsumi / dishonor of their people through the ritual similar to seppuku. Of course there was no real ritual specifically like the one shown, but it takes from that same inspiration.
Now, about the screencap, in Shinto kami are not seen as otherworldly or only spiritual beings. Kami are humans, but also animals, and all of nature. There is simply the physical body (our bodies, animals bodies, the tree itself, the sun itself, the moon, etc.) And the spirit/soul of these “bodies”. Together, particularly awe inspiring or impressive existence, it is called as kami, the physical and spiritual together. Ryukishi may be saying that we make up monsters or spirits to blame our human faults, but not outright denying kami to me. After all, (Higurashi full spoilers) Oyashiro sama as an evil or torture curse kami was fake, but Hanyuu was portrayed as a very real existence, and indeed was a human once herself . Shinto is very in the present/this world, so it can seem less religious or spiritual to other faith paths like Christianity or Buddhism.
I noticed there is a lot of not so much religion but spiritual paths such as Alchemy very strong in Umineko as well. Also of the Golden Dawn and Hermetic paths inspirations, and of course Solomonic magic. Christianity is also a big overtone in Umineko I feel moreso than the Shinto presence. As fits the story it is definitely a more Western spiritual practices feel.
Higanbana is more local folklore of youkai and urban legends but not so much Shinto , Buddhism, or Onmyoudou. There are some references here and there but it is heavily more folklorish than religion. Im not sure about RGD but Trianthology didnt have much religious themes compared to Higu or Umi.