There's nothing "irrational" about them either.
They are inconvenient, uncomfortable, and a needless expense. They force you to button your top button of your shirt in such a way that your neck is constricted. They might drag in your soup. They don't keep you warm. They are an abomination on good sense.
Furthermore, that is exactly why they are worn. It is proof that you thought this meeting was sufficiently significant that you were willing to endure some discomfort.
Moreover, look at neckties from the opposite angle. My software will not work any better if I demonstrate it while wearing a necktie. However, I will sell more software if I wear a necktie. This is utterly irrational on the part of the customer, and yet everyone knows that this is what is expected on the part of a participant in our culture.
I disagree. One is free to choose whether to wear a neck tie or not (I sometimes do and sometimes don't) without fear of scorn or ostracism. Admittedly, one's employer might have a dress code that requires the wearing of neck ties, but that's usually driven by Management's desire for visible outward "professionalism". One is always free to vote with one's feet, though.
This is preposterous. There are indeed people who heap scorn upon and ostracize non necktie wearers. As you note, you don't have to associate with those people, but there might be financial discomfort if you make that choice. The observant Jew is, likewise, free to vote with his feet. He chooses not to do so.
You might think that the analogy is bad, because the observant Jew is under some sort of delusion that God will be angry with him if he pushes that elevator button. That's not really the case. Maybe kind of sort of a little bit, but not really. That's a projection from Christian teaching, I think.
Until I married a Jewish woman and began participating in Jewish ritual and observance, I assumed that Christianity and Judaism had a lot in common. In the "Judeo-Christian" tradition, there was a basic sense of morality, but Jews didn't accept Jesus as the Messiah, episode I. Now I know differently. Judaism has more in common with Buddhism than it has with Christianity. At least, that's my experience of both of them.