I was able to solve the error. I changed:layer = arcpy.mapping.Layer('C:\path\shapefile.shp')
symbologylayer = arcpy.mapping.Layer('C:\path\symbologylayer.lyr')
arcpy.ApplySymbologyFromLayer_management(layer, symbologylayer)
Into:layer = arcpy.mapping.Layer('C:\path\shapefile.shp')
arcpy.ApplySymbologyFromLayer_management(layer, 'C:\path\symbologylayer.lyr')
The former code worked only on my PC, the latter code works on all PCs checked so far.