Muslims are often of a different race than Christians, so conflicts with them risk tarring a person with the deeply insulting label of "racist"

Why don't you use the terms European and Middle Easterner? Christianity as a religion is about as racially diverse as one can get and the same is true of Islam. Imagining a generic "average" global Christian insulting a generic "average" global Muslim and terming that racist makes little sense.

The charge of racism wouldn't be used by a Sudanese or PC minded Kenyan against a Christian Kenyan. In the context of Europe this is employed because of the inter-ethnic conflict present below the surface.