Urine was often used for dying cloth. It isn't effective as a yellow dye, as seen by looking at typical urine stains:
The ring-shaped appearance of urine stains on cloth suggests that the colour is, mostly, not due to the urine directly. If the urine produced the colour, the colour would be deepest in the middle of the stain, where there was the most urine. The colour being concentrated at the edge of the stain indicates that the colour is mostly due to other things that were washed by the urine to the edge of the stain.
So what does the urine do in dying? Urine is used for four different purposes in dying. The urine used is typically stale urine, which has a high ammonia content as bacteria convert the urea in the urine in ammonia. The urine is used for:
Cleaning the fibres or cloth. The ammonia helps dissolve grease, making it easier for the fibres to be dyed. Modern cleaners based on ammonia work on the same principle. Urine was also used for traditional laundering, teeth whitening, and leather-making (where it would help remove fatty residues).
As an extracting agent, to produce the dye. For example, the right type of lichen could be soaked in urine to produce a purple dye.
As an alkali to change the colour of a dye.
As a mordant or fixative to make the dye bind to the fibres. This was especially effective with wool. A mixture of stale urine and alum was commonly used, more effective than either the urine or alum by itself.
Both animals and humans know that urine and excrement aren’t clean
The use of urine by humans for laundering, teeth whitening, hair washing, etc. shows us that perceived "uncleanliness" of urine wasn't a barrier to its use for cleaning. Since urine was widely used to make things cleaner, there wouldn't have been any real barrier to also using it as a mordant or extracting agent or modifier in dying.
Animals don't appear to treat urine as particularly unclean. They use it mark territories, and happily use their noses to investigate it when other animals use it so. Animals also often treat excrement as a valuable or even tasty substance, collecting it as food for their babies, fighting over it:
and so on. The glorious cycle of nature can be readily seen on many farms, with the farm dogs snacking on chicken poop, and the chickens in turn avidly pecking away at the dog poop. Our modern urban sensibilities about these things are not always shared by animals, or our ancestors.
