In my prior post where I said "the UN General Assembly" I probably should have said "the UN Human Rights Council (the U.N.’s main human-rights body)".
To see why such resolutions by the USA are needed, or potentially needed, including opposing efforts by the United Nations to implement an international anti-blasphemy norm, see https://www.huffpost.com/entry/blasphemy-resolution-pass_n_788305 (called "Blasphemy Resolution Passes U.N. Committee") and https://www.nationalreview.com/2011/03/anti-blasphemy-measure-laid-rest-nina-shea/ (called "An Anti-Blasphemy Measure Laid to Rest"). The latter article says the following.
'A long-term campaign by the U.N.’s large Muslim bloc to impose worldwide blasphemy strictures — like those in Pakistan, Saudi Arabia, and Iran — was given a quiet burial last week in the Human Rights Council, the U.N.’s main human-rights body. At the session that ended in Geneva on March 25, the Organization of the Islamic Conference (OIC), sensing defeat, decided not to introduce a resolution calling for criminal penalties for the “defamation of religions” — a resolution that had passed every year for more than a decade. This is a small but essential victory for freedom.
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The OIC’s anti-defamation effort was inspired by Ayatollah Khomeini’s infamous 1989 fatwa, directing “all zealous Muslims to execute quickly” the British author Salman Rushdie and others involved with his book TheSatanic Verses. While not explicitly embracing vigilantism, the Saudi Arabia–based OIC, an organization of 56 member states, quickly endorsed Khomeini’s novel principle: that Western law should be subject to Muslim measures against apostasy and blasphemy.
The OIC worked to institutionalize this principle within the United Nations. By 1999, it began introducing resolutions annually in the Council’s predecessor (the now-discredited Human Rights Commission) to condemn any expression that could be construed, however broadly, as “defamation of religions” — but meaning, specifically, criticism of Islam.
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In 1999 and 2000, the anti-blasphemy resolutions were adopted by consensus, with, inexplicably, the U.S. joining in.
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However, in 2007, support within the Council declined, and the “yes” votes steadily eroded thereafter.'
The article says that resistance to efforts to pass further UN resolutions against defamation of religion were strengthened in part due to ".. the persistent lobbying efforts against the resolution by the U.S. Commission on International Religious Freedom, members of Congress — notably Representatives Chris Smith (R., N.J.), Frank Wolf (R., Va.), Trent Franks (R., Ariz.), and Eliot Engel (D., N.Y.) — and a broad array of non-governmental organizations, from the Becket Fund to Human Rights First."