Also, some service manuals will say to bleed the rear brakes first, while other manuals will say to bleed the front brakes first. As in this case.

The front brakes and rear brakes are basically two separate systems........meaning that the fluid from one side doesn't mix with the fluid from the other. So if one side has air trapped in it, the air won't contaminate the other side, either.

So in reality, it doesn't matter which side (front or rear) is bled first. Unless you want to believe one service manual over the other.