Even if yawning in public affected sexual fitness: how long has it been socially impolite to yawn in public? Evolution takes a rather long time in species with long reproductive cycles. Almost all mammals yawn, it would take significant genetic changes to breed that out of us. That doesn't happen overnight.
No, it isn't. It can be socially impolite to yawn unexcused, when someone is talking to you, as it has come to be interpreted as boredom rather than tiredness or similar. But it isn't inherently impolite to, for instance, yawn when walking down the street, or in a setting where someone isn't talking to you.
Is that the right criteria? A trait must be completely, 100% disqualifying as a mate or else it sticks around?
Our ancestors used to have tails. We no longer have tails. Plenty of people wear artificial tails today and get laid, it's not a 100% disqualifying trait
Our primate ancestors required tails so they could effectively move around on trees. A tree dweller without a functional tail is slower and has a harder time gathering food and escaping from predators. That's a very strong selection pressure that ends up maintaining the tail.
When the woods in eastern Africa changed into savannah, we shifted to two legs and adopted a persistence hunting strategy. The tail became useless, even a liability, and mutations that resulted in reduced tails were not selected against anymore.