This is not at all an attempt to banish infinity in any general sense.

Of course it is. Nothing infinite has been spotted so far.

I'm not sure how your sentence is a response to my sentence.

This is rhetoric without content.

Is it? Is this same "rhetoric" against aliens also without a content? If I say that people want aliens, because they have lost angels, is this really without a content?

Not only that there is no infinite God, even infinite sets are probably just a miracle.

Generally, yes, the content level is pretty low. It essentially amounts to Bulverism, where one is focusing on claimed intents and motives rather than focusing on the substantive issue of whether there's an inconsistency in PA or ZFC that can arise due to issues with supertasks or other ideas related to infinity.

It may well be that specific people or groups are adopted aliens in a way that is essentially replacing deities. The Raelians and other New Age groups certainly fall into that categoyr. But it is a mistake to therefore claim that in general, people believe in aliens as a replacement for belief in a deity. And it is an even more serious mistake to make such claims about infinite sets. If you see physicists praying to infinite sets, or claiming that infinite sets are responsible for the creation of the universe or humanity, or claim that infinite sets will somehow save us, or claim that infinite sets have an agency to them, or claim that infinite sets have a special mystery and majesty to them that merits worship, or if they start wars with or excommunicate people who don't believe in infinite sets or believe in a different type of infinite set, then there would be an argument.