I see cycling advocacy as a trinity of advocacy. The first aspect of advocacy entails enocuraging more people to ride and get out of their cars. To the extent this necessitates persuading other people, there is some political hue to the first aspect. The second aspect invovles educating the public about cyclists' rights, which includes the first aspect. This too involves politics indirectly, only insomuch as by educating the public as to cyclists' rights you may make the first and third aspects easier. The third aspect invovles "lobbying" for political change at the local, state, and federal level. This " pure political" aspect of advocacy includes everything from supporting or oppossing legislation to becoming involved in local financing and design decisions concerning roads and other facilities.
It all depends on how you define "politics." If your definition is limited to supporting or opposing specific legislation, then only number 3 consitutes poltical advocacy. If, however, you define politics to include all instances in which you seek to persuade people to change their behavior, then one must acknowledge some political aspects is numbers 1 and 2.