Here is the better explanation. In terms of the block-Earth system, both gravity AND friction should be thought of as internal forces, as both are forces between the block and Earth.

Typically we don't think of friction this way because it is non-conservative (no associated potential energy with it) but for this system that is the easiest way to consider things.

Note: I also think it's useful to consider the case of NO friction here. For many conceptual problems like this, the "edge cases" can help, as "no friction" is approximately the same scenario as "very little friction", so the answers should not change much. In the no friction case, I think it's fairly clear that (by conservation of momentum), the Earth's momentum is NOT constant. In fact, this scenario might be simple enough to go back to very basic principles. By Newton's 3rd Law (or just definition of force of gravity) the force of gravity on the block is equal and opposite to the force of gravity on the Earth. Hence, both objects are accelerating so both objects have a change in momentum.