Will 2x6 cedar be ok for monkey bar rails?
For one Western Red Cedar 2x6 plank, loaded vertically, attached to bombproof supports at either end:
The estimated sag is about a quarter inch in the center, and the shear is 1.39 MpA.  Materials data gives me an approximate Shear strength of 5.5 MpA, so you're well within limits.
HOWEVER, the weak point will be the attachments. These will need to be rigid in shear and in bending.
As well, you'll need to design the beams each plank is attached to to support the full load.
8 feet is an invitation to overloading.