Amid a surge of anti-gay violence and repression in several countries, the United Nations’ human rights office on Friday launched its first global outreach campaign to promote tolerance and greater equality for lesbians, gays, transgender people and bisexuals. Called Free & Equal, it’s an unprecedented effort by the Office of the U.N. High Commissioner for Human Rights to change public attitudes around the world on issues that have bitterly divided the U.N.’s own member states. The multi-pronged campaign—announced at a news conference in Cape Town, South Africa—will include videos and public-service announcements distributed through social media, a new website, a...