This question already has an answer here:
The radian is defined as the ratio of the circumference and the radius. Both are measured in meters. So there should not be a unit for that. But we use 'rad' as the unit of the radian value.
The coefficient of static/kinetic friction also the same, it is a ratio of both forces. Therefore it doesn't have a unit.
So, is there a special reason to have a unit for the radian value?