My wife's hair totally clogged up our ensuite shower within a few months of moving into the home.Because I did not want to touch the guck, I actually tried 2 different brands of drain cleaners (Drano and maybe Liquid Plumber) but they did not work.
Then I fashioned a vintage metal clothes hanger into a clumsy tool .. which still works to this day.
P.S. I also put a strainer designed for kitchen sink on the shower drain to catch most of the hair. But some hair still slithers through the round holes.