Britain was on a knife edge when Lucy Connolly, a mother and former nanny, tapped out an inflammatory 51-word post on social media a year ago, calling for “all” hotels that house asylum seekers to be set on fire. “If that makes me a racist, so be it,” she added, a postscript that did nothing to spare her the wrath of the country’s courts. Now serving a 31-month prison sentence for inciting racial hatred, Ms. Connolly has become a charged symbol in a debate over whether Britain is suppressing free speech. Last month, an appeals court refused to reduce her sentence, drawing angry protests from her defenders, mainly on the political right. Critics, including Vice President JD Vance and Elon Musk, accuse Britain of backsliding in the age of social media.