Partner (who knows about these things) used the word 'disastrous'.
o The colour will be very pale (e.g. pastel blue from a navy dye). o The rayon will probably absorb much more than the polyester. o The imperfect mix of polyester/rayon inherent in the fabric is likely to make the result patchy. o Even if it initially looks relatively OK (or at least acceptable), it will tend to wash out fairly quickly.
Partner would not attempt it - just a waste of money on the dye.
If you are nonetheless desperate to try, a dye from a specialist supplier (rather than the usual high street Dylon) might be a better choice.
E.g. (a good supplier but without knowing anything about the specific dyes listed on this page):
But let us know what results you achieve if you do go ahead.