Unitarian Universalism springs from sources – many tributaries flow into the river of the faith we share. The longest and largest source for us is Protestant Christianity, with more recent contributions from Humanism. The Muslim influence on our development has never been huge, but it has played a role.
For example, on our Universalist side, there’s George de Benneville, born 1703. While sailing to America, De Benneville was moved and impressed by the kindness and caring he encountered in some Muslim Moorish sailors on the ship. The experience helped open de Benneville to open-minded exploration of religion. His long and colorful spiritual journey led him to Universalism – the view that all souls were saved – which de Benneville was the first person in colonial America to openly teach.
On our Unitarian side, Islam, or Mohammadism as it was typically called, played a role in our early arguments about the trinity. The early Unitarians, in developing our tradition of freedom, reason, and tolerance, got their name from their critique of trinitarianism. They were Unitarians, saying God was one, rather than Trinitarians, saying God was three. In that debate, the Unitarians sometimes pointed to Islam, which is also unitarian, as evidence that, however faiths may differ, the oneness of God was a natural and reasonable conclusion. In the later 1800s and into the 1900s, Islam remained a frequent topic of Unitarian discussion. While these discussions were often critical, gradually a growing number of Unitarians found much to admire in Islam, and Muhammad’s image among Unitarians was progressively rehabilitated.
http://transientandpermanent.wordpress.com/2010/09/11/muslim-influence-on-the-roots-of-unitarian-universalism/, where more info is available. Thanks to James Ford for this link.)