WTF are sensitivity readers?
They are basically communist censors, but lame. They are supposed to read stuff corresponding to their demographic (gay, black, autigender, etc.) and offer suggestions to improve the text and weed out or correct things which could be offensive. Employing sensitivity readers is increasingly mandatory at publishing houses.
How does one actually make a career out of that?
It is more of a "gig economy" hustle than a career. Monetised twitter nitpicking for the quasi-unemployed, basically.
What kind of education does it require?
Unlike OG communist censors - who were usually very learned men and women from the higher ranks of the cultural elite - the only qualifications are "belonging to a demographic" and "being part of the rainbow brigade" (obviously). They are nobodies, and their opinions are by and large worthless, or worse.