Congratulations on recognizing the imcompatability of bare cedar over Tyvek. That puts you in the minority.
First, you can avoid the issue by using tar paper instead of Tyvek.
If you still want to use Tyvek or some other kind of spun poly housewrap, you do need to keep the bare cedar off the Tyvek.
With the shakes, it's often easiest to do this either by using a product like Cedar Breather between the Tyvek and the shakes, or by running horizontal furring strips, spaced as required by the size and spacing of your shakes.
With the claps, if you are painting or using a solid-body stain on the claps, you simply have to backprime the claps. All that means is that when you prime the show side of the claps, prime the back as well ("backpriming").
If you are going to let the front of the claps go au natural, then you shouldn't do anything to the back. In that case, yes, you can furr them out. Run your furring strips (often times mason's lathe is used) vertically, one over each stud. This does increase the thickness of your wall assembly a bit and requires a bit more detailing on your corner boards and fenestration.
The furring out for the cedar is often called a "rain screen." Even when backpriming, it's an additional detail used in high wind, high rain areas...like coastal climates...where horizontally driven rain could be driven behind the claps. It's another detail used to help shed water.