ehhh, for a lot of traditional Catholics neither Thiel nor Rome are Catholic currently so I think there would be disagreement with both sides here
I thought Thiel's argument was that the anti-AI crowd might tend towards a pagan primitivism (like with mentioning those like Greta) and authoritarian measures to stamp out technology with an Anti-Christ leader, emphasizing base physical pleasure over technological "progress". I guess that's one "End Times" possible trajectory.
Catholicism's not necessarily really for or against (classically) liberal democracies, with exception of specific configurations that might be condemned afaik with books like "Liberalism is a Sin" (liberalismisasin.com) or writings against the "heresy of Americanism".
The Vatican could have pointed to Catholic views of prophecy, like Rev. Huchede's "History of Anti-Christ", so people might compare views being presented: https://archive.org/details/huchede-history-anti-christ-best...
p. 11 says, in contrast to a top comment here that claims there is no singular Anti-Christ figure: "the Sacred Scriptures speak of Antichrist in various places as being a particular person or individual."
Rome has been thought to have fallen to modernism with the Vatican 2 changes, which sets them up more for accepting or bringing about the rise of an Anti-Christ movement in the views of some traditionalists
(can elaborate on anything if anyone requests it)