I have used rayon since 1992 when I bought my first embroidery machine and embroidered towels I still use. The colours are fine after years of laundering. But then there's no bleach in washing powders / liquids in my part of the world and I never use bleach for stain removal either.
I found out the hard way that there is bleach in some dish soaps!
You are confusing rayon with polyester thread. Rayon is NOT bleach resistance while polyester is. Below is a link to a statement by Superior Threads documenting why they do not have a rayon thread line.
I read somewhere that their rayon thread was bleachable. I just don't remember where. Sounded crazy to me, but was hoping someone might be using this thread and let us know if the thread actually stood up to bleacing.
Whose Thread? I would recommend contacting the supplier prior to ordering.