Brother, you said it.
I don’t think the point was that the two beliefs are exactly equivalent. Just that the justification given for a belief that ETs are visiting Earth could be given in support of any obviously false belief. The Santa Claus example is maybe a bit of a cliche, but the reason it’s used is because most adults agree that it doesn’t exist. If you can use the same arguments to support something which is evidently not true, what is the use of those arguments in deciding what is true?
When you admit that you have insufficient evidence to objectively justify your beliefs, you are saying that you don’t care whether or not they are true, you just want to believe them anyway. That’s fine, but don’t expect anyone else to take that position seriously or treat it with any respect. It’s not a ‘different kind’ of reasoning it’s a declaration that you are unreasonable and that your opinions can be dismissed without investigation. By allowing faulty reasoning, logical fallacies and low standards of evidence to replace reason, empiricism and objectivity, you abandon any credibility your claims might have. It’s not ‘delightfully quirky’ to think that 2+2=7. It’s not ‘a different sort of arithmetic’. It’s wrong.
If you want people to respect your ideas, you have to justify them. You can’t have the best of both worlds, believing implausible things without justification and being taken seriously. Pick one.
From my perspective, it is weird in the extreme to attempt to believe things which are not evidently true. You seriously underestimate the beauty and profundity of reality as it is, when you cast aside the only reliable mechanisms we have for separating truth from fantasy. The products of puny human imaginations, be they ghosts, gods, vampires or flying saucers are small and childish and dull by comparison to what is really out there. None of them are real. Get over it. The things which really are real, the things which actually exist, are way, way cooler.
I can see some aliens might have left some sort of automated monitoring device for say some sort of interstellar anthropological study.
Which is why I wish we would send a ship to investigate the black knight.
I think a public demonstration of some sufficiently advanced technology would be enough to convince me. As others have stated there isn’t a shred of evidence that we’ve been visited and the odds are pretty slim that it will ever happen. That said I have some relatives that claim to have touched a landed craft in their childhood and they still believe it happened to this day. But that is just the thing, we plenty of stories, but no one can produce anything to prove it happened.