I nominate our opening salutation to letters. I write “Dear Mr. Smith” to a business associate. There is nothing “dear” about him. I don’t mean to convey love or affection. But I say it because we are supposed to do it.
Does anyone have something to top that as a “we only do it because”?
Handshakes were originally done in the middle ages to prove you were unarmed.
Religion however seems like the most antiquated. If there is a custom that is older than 2000-4000 years old that we still engage in I don’t know it.
We still exchange money for sex.
Public executions.
Blessing someone after they sneeze. What other bodily functions do we publicly draw attention to by invoking the protection of a deity?
To the extant that antiquated means “outdated”, I think of it as referring to things that no longer have value. Since religion and sex both make people happy, I’m wouldn’t call them antiquated.
Handshakes was my thought. I believe the are antecedents to the middle ages practice going back at least to the classical era.
Caring about virginity, or sexual purity. Even so called atheists still care, and I’m not even talking about infidelity or cases where paternity is hard to establish.
Right. I didn’t mean to make this a “real” debate about meaningful things.
Handshakes could be replaced by something else, but what? In my OP, the word “dear” could easily be replaced.
“Bless you” upon sneezing is a very good counter. After all, when a friend has a bout of diarrhea in the downstairs toilet, we don’t call out “bless you” with every subsequent blast of flatulence.
I would also nominate calling every old man “sir.” It’s a show of respect just because of his age. He might be a miserly, miserable old child molester, but we give him that title of respect, but a 30 year old decent man we don’t.
There’s the Thai wai, the placing together of the hands in front of you with a slight bow.
Plus chances are he has never actually been knighted by an English monarch.
Sex. OHGODOHGODOHGODOHGOD!
I’m not sure that’s for invoking protection.
No, but it can certainly count as a mystical moment. If done right 
And it counts as “repentance” if it was done at a high level of wrong.
For men: Mr.
For women: Miss or Mrs. depending on whether or not they are married.
While the Miss/Mrs. distinction is particularly antiquated the Mr. vs Miss/Mrs. distinction also is antiquated–why a need to make this distinction here? Why not just M. Jones (the person whose last name is Jones) and M. Smith (the person whose last name is Smith).
And of course there are a zillion sex based names (actor vs actress), which are likewise totally antiquated.
I nominate the tie. Basically wrapping a bit of cloth around the neck, but for what purpose?
I note with interest that many of us who are employed in the newer technologies no longer wear ties. That most conservative of all ventures, banking, still wear ties, but so do car salesmen and (usually) real estate salesmen, lawyers and politicians.
I nominate standing for the anthem, and stopping in the street for a funeral procession. My bet is they precede niceties like a blessing after sneezing, or Mr & Mrs titles.
Are “Miss” and “Mrs.” still used all that much any more? They’ve been replaced to a large extent by “Ms.”, at least in the professional world.
Buzz. 
I disagree with your nominations because those two things serve a knowing purpose. First is standing to show patriotism and the second is to convey respect for the recently departed.
I agree with the nomination of the Miss/Mrs. distinction. Although it does specify whether the woman in question is married, there is absolutely no need to make such a distinction in a salutation.
I’ll rank the submissions in the following order:
)First of all, your OP didn’t mention cannot ‘serve a knowing purpose’.
Secondly, how is ‘Dear’, Mr or Mrs not a demonstration of respect like stopping for a funeral procession?
I’m out!
Why is it patriotic to stand and respectful to stop for a funeral procession?