Never tested the theory have you. It doesn't speak to orbit of planetary bodys, it's a general principal. line the inside of a centrifuge with spheres and cap it. Spin it up, pull the top and note the action of the spheres, they launch out spinning in the same angular motion as the centrifuge. That is the conservation - whatever is launched out carries the same angular direction as what launched it. In a frictionless environment, this will be unaffected and unchanged over time.
In the case of encountering friction, the spin should come to a halt. That is your problem. You have retrograde moons, planets, galaxies, etc. Gotta account for that somehow or the big bang is nothing but a big dud. And you guys know that.
The angular momentum of an isolated system remains constant in both magnitude and direction. The angular momentum is defined as the product of the moment of inertia I and the angular velocity. The angular momentum is a vector quantity and the vector sum of the angular momenta of the parts of an isolated system is constant. This puts a strong constraint on the types of rotational motions which can occur in an isolated system. If one part of the system is given an angular momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same angular momentum in the opposite direction. As far as we can tell, conservation of angular momentum is an absolute symmetry of nature. That is, we do not know of anything in nature that violates it.
Please note: The above does not say everything has to be spinning in the same direction. It says that any change in the rotation of an object within a system must be accompanied by a change in the rotation of another object in that system.
Your pissant version of the Conservation of Angular Momentum can be shot down simply by looking at some of the retrograde moons in the Solar System.