Did the GP explain why the CFS consultant 'rejected' you?
I see it as a positive, although it is annoying you have to wait even longer to see a rheumy. The fact you've been re-referred suggests the CFS service looked at your referral/results the GP sent and decided you don't entirely fit the possible CFS diagnosis. They must think a rheumatologist can help you or is best suited to help you. Perhaps rheumatological explanations for your symptoms need to be ruled out.
I have been rejected by the CFS service too in the past - I'd already had M.E. for 18 years at the time this happened, but I had worsened a lot. Unbeknownst to me, I had another major health issue that needed to be dealt with, and the CFS consultant realised this and wrote to my GP asking them to send me to a different specialist. I was glad that she had picked up on it and didn't just get to blame everything on CFS (which can happen).