A good green can be made by taking copper placing it in a sealed crock with strong vinegar and burying it in a dung heap for some months, the dung supplies a constant heat source which speeds up the chemical reaction. This what my icon painters directory tells me is the best way of producing green. Of course green can be obtained from vegetable sources but in tends to be fugitive.
Most colours come from minerals, mainly clays and are in the range of yellows, browns and reds, even a rather pale blue, you just need to spend a great deal deal of time grinding.
Blue could be made by grinding lapis lazuli from Afghanistan but it was more expensive than gold.
Mineral colours are fine for painting because they are held in suspension but for dying cloth you need the colour to penetrate the fabric therefore it needs to be totally soluble. Therefore vegetable dyes tended to be used, the problem is that they tend to fade. What was available tended to determine liturgical colours.
Black was a natural colour, black wool came from black sheep or goats, it could also be obtained from, squid or octopus, or vegetable galls though it would have tended to be black red/green/blue rather than a solid black. Black ink was used in thimblefuls, black dye needed to be used by the barrelful.
White came from the natural colour of the fabric, and from removing colour, bleaching, the problem with white was keeping it clean. Any decoration would tend to be bleached by cleaning it. It was literally a non-colour.
Greens were made from verdigris, as in the process above, but also from lichens and other vegetable sources.
Red was more problematic, its source was either the crushed cochineal beatle, which gave a deep red that was quite colour fast and bright, or else from the madder root, which gave a deep pinkish red but tended to fade over time.
Urine, either animal or human, gave various reasonably fast colours ranging from pale yellow to orange or even an orangey-red, by feeding animal on various food stuffs the colour coul be changed.
A sort of purple/red could be produced by beets, it could be brightened by mixing it with urine or lichen, but I think the deep purple of the modern beetroot wasn't widely available.
Blue was widely available but it tended to be rather dark, the colour of jeans, from woad or later indigo, it was used in the Sarum Rite for clergy dress; "blue cloth" was a major English export.
Blue, yellow, green, russet, brown vestments seem to have been common vestment colours in the dissolution records of monasteries and churches.
The ancient precious royal colours of royal blue or purple made from crushed and fermented molluscs or deep red from the cochineel beatle were very expensive, it wasn't until the industrial revolution that these colours could be produced cheaply, bright purple seems to have been the most difficult, as opposed to muddy violet.
The liturgical colour white until the 15th century, at least, was unlikely to have been plain white, an alb could be bleached, a chasuble or other vestment would have to be stripped of its decoration before it was cleaned, hence it would be more likely to be a pale version of another colour. Its preciousness came from the care to keep it pristine. Black was much easier to deeal with, it simply didn't show soot and sweat and grime. Hence its use for Requiems and mourning, it was cheap and easily cared for.
In the East white was used for the same purpose but devoid of decoration, untreated cloth or simply bleached.
All this is really to say that the rubric for Requiem Masses calls for either black or purple, or white to be used. I have always presumed white was for Asian communities where white is the traditional colour of mourning, it is not "festal" white but dull and unembellished rather like the unbleached Lenten array of Sarum use.