Paul said we are to greet one another with a holy kiss. I've seen Christian men that won't even give a hug where as women I've seen a hug as a way of greeting each other. Women seem more comfortable showing physical affection vs men.
I don't think its wired as much as it is cultural. In the states its something that goes back centuries. Probably won't change in our lifetime but that doesn't mean you don't try to change it with one person at a time.
You're only considering the edges of stereotype. It's useful to note from culture to culture and century to century what changes and what
doesn't change. The fundamental strands of male and female behavior are the same from culture to culture and from century to century.
"Husbands, love your wives."
"Wives, respect your husbands."
I work with teenagers, and I've noted that when a young man makes a really stupid decision, it's almost always about
respect--to gain respect, to prevent disrespect, to be worthy of respect.
But when a young woman makes a really stupid decision, it's almost always about
love--to gain love, to prevent being unloved, to be worthy of love.
Such things have not changed in two thousand years.
A bit ago, there was an experiment done with bonobos (a chimpanzee-like ape) in which children's toys--dolls and toy trucks--were left among the apes. The male apes took a minor initial interest in the toy trucks, simply as "strange new objects" for a while, but took no interest in the dolls. The female apes, however, took a great interest in the dolls, ignoring the toy trucks.
Of course, the toy trucks represented nothing to the apes, but the dolls had a similarity to their own infants. What was interesting is that the females picked up on that similarity but the males did not...and that has been replicated many times with human children.
There was another study of infants in newborn nurseries that noted female babies cried sympathetically (that is, when another baby began crying, it tended to set off crying in female babies nearby) but male babies did not.