Nope it's not gender thing. It's more of a common sense thing.

A shower get you wet all over quickly and makes you FEEL clean.

A tub lets the dirt soak off and makes you REALLY clean.

If you tub fairly regularly you shouldn't have too much of a problem with built up crud. I like a tub every day, but on sometimes have to go a day or two. After a good clean in a tub it takes at least three days before the human smell kicks back in and a day or two more than that to get really stinky.

If you wash your hair FIRST, then you shouldn't have any problems, other than it's not so much fun to relax with wet hair.

Showers were rare in England when I was there (I left in '73) because
the water authorities required a header tank for a water heater and it was illegal to connect your possibly contaminated header tank (it was usually up in the loft and could, and sometimes did, contain a dead rat) to the authority's nice clean cold water supply.

So, many showers in those days were illegal. I don't know how things have changed since I left.

Regarding temperature differences when sharing. Yes, they do occur, but the benefits usually outweight the discomfort.