Just to be clear. I understand that tzinuys is important and certain things it is intended to protect against are yeherag val yaavor. However, that is the fundamental question. What falls under the tzniyus umbrella (or as the discussion has veered, the niddah umbrella).
Remember, this thread is actually about giving women car rides, not mixed dancing, and presumably it is possible to do that without touching.
In any case, I do not agree with your absolute statements, but you are entitled to them.
Socializing as you point out is completely different, but yet originally you lumped them together in your post.
According to ramban and others, even hugging and kissing is assur only derabanan. So again, an issur derabanan can hardly be said to be the defining trait of judaism. Rambam says differently, but even rambam is generally understood to be talking about intimate touching.
As (almost) everyone in the US my age with any knowledge of torah knows, R’ Moshe said subway touching is ok, but handshakes he was uncomfortable with. But even R’ Moshe acknowledged that touching that is deemed by society as not to be affectionate might be ok, the question is what falls into that category, and many other issues. And I have already gone on too long.
Anyway, my point (and its a point others have made in other contexts) is that halacha has many viewpoints, so to come on here and make absolute statements, it would be preferable if you said “my opinion.”
That said, maybe I am being ridiculous. It is an internet board after all, so perhaps that it is your opinion is implied.