CX doesn't require you to fly their metal to gain the next tier, but that comes at a cost. Like BA, CX uses a Tier Point System (or in this case, Club Points). You are awarded less tier points flying on non-CX OW partners, and in some cases, it could be significant. For instance, flying BA F LHR-HKG earns less CPs than flying CX discounted J.

Also, I should add that they charge USD100 for membership.