Since you are recommending it, I assume they don’t bash Conservatives (either directly or indirectly). Also, that they don’t show 1953 London as a multi-cultural mecca.
No, there is no conservative bashing. Nor does the film dwell on multiculturalism. It is set in the 1950’s London theatrical district and is culturally attuned to that milieu. Inspector Stoppard and Constable Stalker are both police officers of vaguely middle or working class origin who are strangers in a strange land when they encounter the theatrical swells, who are all of much higher social status. But this is not a film about class differences either; this is just a matter of getting the characters’ mannerisms and accents right. One of the charms of the film is that Saoirse Ronan gets to unleash her inner Irish to full effect.
There are several black actors, two with substantial supporting roles, but they are both very proper and British in presentation. David Oyelowo plays a very fussy, theatrically traditionalist playwright named Mervyn Cocker-Norris, who is gay but still tries to pass off his tall Italian boy toy as his nephew. He becomes one of the suspects and is hilarious. (You see him in the trailer.) But this didn’t strike me as racial stuntcasting. British movies nowadays have pretty much gone to colorblind casting. That’s ok with me, especially for entirely fictional characters; historical characters are trickier.
To get 1950’s London theatrical culture right, you would need some light in the loafers characters around anyhow. The movie makes one of them black.