Is it possible to dye synthetic fabric without patches appearing?

Answer 1

Ordinarily synthetics must be stripped of the original color in order to have a successful re-dye process.
And bear in mind that white is also a "dyed" color, not natural.

If the fabric is Polyester or Polyurethane, you won't be able to strip the color. They are usually solution dyed, like a carrot, the color is all the way through the fiber. Most nylons are dyed like a radish. They are dyed after the fiber is in a solid state and the dye only penetrates the fiber to a shallow depth.