Any original WWI slings I have seen were the tan colour. I was told that the standard webbing kit at that time was the Pattern 1908, superceded by the Pattern 1937, superceded by the Pattern 1951.
Any unaltered web gear I have ever seen was tan, or else was tan originally and then blancoed until it was something else, apart from belts, web, Pattern 1937 and gaiters, armoured troops, for use of.... which were black and you needed that blasted Salvator for them. I HAVE had blue Air Force web gear: rifle sling, revolver holster, but it is scarce.
I have no idea precisely when the web sling was introduced for the LE rifle, but have always assumed it to be part of the P. '08 kit. Will somebody kindly give me a pat on the back if I'm right.... or jump all over me if I am 'way out to lunch (again). Thanks.