The following is no more than a brief mental tally based on my own viewing experience rather than facts and figures, and since I'm by no means the biggest film or TV watcher out there, I'm very open to correction. (I'm putting theatre to one side, as I have a feeling the answers may be significantly different there because of the history of the genre.)
Are women played by women? Pretty much 100% of the time.
Are black people played by black people? Pretty much 100% of the time (and the same goes for other racial groups, although not nationalities).
Are working class people played by working class people? Often, but by no means invariably.
Are gay people played by gay people? Sometimes, but by no means invariably.
Are trans people played by trans people? Very occasionally, but never in major roles and often for the purposes of fetishistic transploitation.
Are wheelchair users played by wheelchair users? Increasingly so, but I would guess still less than half the time.
Are blind people played by blind people? I actually have no idea how often this happens.
Are dwarfs played by dwarfs? Sometimes, but see the caveat for trans people above.
Are people with Down's Syndrome played by people with Down's Syndrome. Invariably, I think.
Obviously other categrories could be added, but even getting this far makes me aware of a) how little I actually know about casting practices, and b) the wide and puzzling variations within the list. Why is it unthinkable to have a character with Down's played by anyone other than an actor with Down's, but perfectly thinkable to do this with blind people or wheelchair users, for example? Fairly common to have gay characters played by gay actors, but almost unheard of to have trans characters played by trans actors? Is there any rationale at all here? Or is the landscape as confused as it looks at first glance?