It’s not recommended to blast after anodizing for the obvious reason that you will remove the anodized layer. Even if you’re careful with light blasting, the anodized layer will still be damaged, and you risk getting some inconsistencies in color. Remember that the anodized layer is only microns thick, maybe in the range of 10-20 microns.

Also, since you’ll be dyeing the parts blue, I assume you’ll also have applied a seal layer after dyeing. That seal will not survive the blasting, so even if your immediate color is acceptable, you’ll experience color fading and wearing over time.