I'm not sure if Gen Z is going to trend conservative in the traditional sense of the word, but what is observable is that they are trending to the right of the Millennial cultural zeitgeist, which isn't that hard to do. The Millennials are infamous for their tendency to lean far to the left on average, partly because of the cheapening of academia and partly because they are responding to the legacy of the Religious Right Boomers and the more centrist and relatively apolitical Generation X.
The Millennials went far left as a way to rebel against the religious conservative Boomers and the more moderate Gen X.
Since the Millennials dove headfirst into militant atheism, intersectional queer feminism, Anarcho-Communism, and in the most severe cases, virulent racism against whites, you can't really rebel against that by going further left and the fact that Millennial leftism is celebrated and enabled by neoliberal corporatists sort of goes against the whole rebellion image. The modern Millennial Left are useful idiots and your average Zoomer knows this.
How do you rebel against something like that? You go further right. And by that, I mean going to the right of Lenin, Mao, and Trotsky.
The whole "Generation Zyklon" meme is nothing more than wishful thinking, but the Zoomers are swinging hard against the SJW zeitgeist that the Millennials have established. Most Gen Z kids hate the SJW's. The only Zoomer SJW's I've seen are the ones who are old enough to be part of that "in-between" group that overlaps with the younger Millennials.
They don't want to be like the SJW's, but since the Religious Right still exists on a regional level thanks to old incumbent Boomer geezers and is still invoked as a straw boogeyman by the SJW Left, they don't want to go in that direction either.
The Zoomers hate the SJW's, but they also hate the remnants of the Neocons and Evangelical fundies. Overall, they are a lot more centrist or moderate liberal in their leanings, sort of like how the old Gen X'er Left was in the 1990's and 2000's and the more right-leaning Gen Z kids tend to strike me as more libertarian conservative or "South Park Republican" as opposed to the "Murica and Jesus" redneck Boomer conservatives.
A lot of the clickbait mills give conflicting stories on how Gen Z feels about the LGBT community. Some articles say that they are more pro-LGBT than even the Millennials, while others start doomsaying about how LGBT acceptance is lower among the Zoomers. That seems to be a contradiction, but it isn't.
The Zoomers are probably very much in favor of the LGB, but don't support the T or the Q. The Q is a non-issue that has no place in the movement (basically straight Millennials LARP'ing as "queer") and the T are heavily associated with the SJW zeitgeist.
Nobody wants to have their favorite games, shows, and movies "cancelled" because some whiny pretentious troon got butthurt and screamed about how it was "problematic"
Gen Z is going to lean right for the most part, but I highly doubt they will lean towards the Religious Right or the Alt-Right.