Thank you for the knowledge.
Since ideologies are based on secular beliefs--such as secularly believing in equality and "Natural Rights"--they are in effect secular religions. (Marx was a failed materialist but a hell of an equalitarian.) Political parties are the products of ideologies. Being a member of a political party and being a member of a sacral religion is in no meaningful way different from being a member of two different sacral religions. It therefore seems to me that the Catholic Church (and for that matter all religions) would bar members from joining political parties. That would not preclude participation in the political process, but it would emphasize the dominion of faith over all things political.