Yes, Evangelicals and Muslims compete, but they also do talk.
In April of 2020, leaders of the World Evangelical Alliance and Nahdlatul Ulama — including Dr. Thomas Schirrmacher, Dr. Christine Schirrmacher, Dr. Thomas K. Johnson, Kyai Haji Yahya Cholil Staquf and C. Holland Taylor — established the Humanitarian Islam/WEA Joint Working Group. This volume is a product of the Joint Working Group’s Subcommittee on Jurisprudence, Human Rights and Ethics.
Founded in 1846, the World Evangelical Alliance is the largest international organization of evangelical churches, representing over 600 million Protestants and national evangelical alliances in 140 countries. It refers to the Gospel of Jesus-Christ as the main teaching, and promotes faith and evangelism through local communities.
Nahdlatul Ulama (NU) federates 90 millions of Indonesian Muslims, and develops within its ranks a movement called Humanitarian Islam, rooted in the principle of rahmah — stressing the need to contextualize and adapting Islamic teachings, while presenting Islam not as a supremacist ideology or vehicle for conquest, but rather, as one of many paths through which humans may attain spiritual perfection. Link