My fact-checking can confirm that this claim is true. BBC has also written an article about the development at this link: Camden People's Theatre: Job advert terms 'position people as inferior' - BBC News
Although neither The Independent nor BBC include a link to their primary source in their articles, I found the old job posting on the Camden's People's Theatre site for employment vacancies, and all of the information/screenshots featured in either article match the website, barring the line in question about "working-class, benefit class, criminal class and/or underclass." However, The Independent did claim that the theatre referred them to an apologetic statement which included a "review of [the wording's] use." Considering the nature of the turmoil, it makes sense that the theatre would have edited this line out of their job listing. The old listing can be seen here:
Vacancy: Artistic Director & Joint CEO | Camden People's Theatre
Finally, I evaluated the credibility of both The Independent and the BBC as news agencies using one of my favorite fact-checking tools, Media Bias/Fact Check: Media Bias/Fact Check - Search and Learn the Bias of News Media
This site rates the BBC's factual reporting as "High." The Independent's is "Mixed," which should generally alert readers to the potential for misinformation. However, much of the information in The Independent's article--most significantly, the line in question--is mirrored in the BBC article. Taken together, this evidence points to the story about the Camden People's Theatre being true.
