Leftish points for cycling: saving the environment, minimal fossil fuel use, reduce motorized vehicle dependence, closer to nature
Rightish points for cycling: Freedom to travel, individual effort, great outdoors, self-supporting, reduces costs
...and all the centerish stuff too.
Regrettably, people can make the "bike-left" assumption. In my usual riding group, we have a whole range of viewpoints from mid-left to seriously conservative. Same at the co-op (in spite of it being an anarchist co-op, a few rightists like the volunteering and playing with bikes). But in all these groups we get along, and try not to get under each others' epidermii.
At the national level, though, the skew is different, especially with "full-time advocates". I remember the keynote speaker at the ProWalkProBike conference in Victoria BC in 2004, who took it upon himself to disparage the then-current occupant of the Oval Office. He then caught himself, and asked: "How many Republicans / Conservatives in the audience?"
Three of us raised our hands - and we were all sitting together.
