Twitter Inc. has taken the bold step of permanently banning conservative blogger Milo Yiannopoulos under its abusive-content policy, fueling a fierce debate about freedom of speech in the social-media age.

The company’s suspension of Mr. Yiannopoulos, tech editor of conservative site Breitbart, came after he sparred with actress Leslie Jones on Twitter this week while users deluged her account with racist comments and hateful memes related to her new movie, “Ghostbusters.”

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