‘Modernist Muslims’ refers to people who believe that Islam (and not merely Islamic civilisation and culture, but Islamic doctrine and law) should be updated to correspond to Western values. This is universally rejected by other Muslims. They are up to 1% of the ummah. Although the West has been encouraging it (together with outright secularism) for several centuries, it is hard to find a believing and practicing Sunni Muslim who adheres to modernism.
At any rate, it has less than 1% following in the Sunni world, and not only no traction but no potential. When Western powers or institutions try to encourage modernism, this only feeds fundamentalist conspiracy theories.
A Thinking Persons Guide to Islam: The Essence of Islam in Twelve Verses from the Qur’an – 2017, by H.R.H. Prince Ghazi Bin Muhammad, page 238