I'd say that bicycles have a huge role in transitioning away from fossil fuels. "Cyclists", however, not so much.
The distinction really comes down to perception. At this point, there is no American that doesn't know bicycles are a thing you can use that can take you from one place to another. While cross continental rides are nice for showing off, someone riding a bike from Anchorage to Albuquerque really doesn't do much to tell common people that maybe that dusty bike in their garage can be used to get their groceries (or at least, not any more than climbing Everest tells people that you can walk to the store, even if it's uphill). You need to show people that they can do normal stuff with their bikes.
Which is sort of where cyclists -- defined as skinny dudes in Lycra (as about 97% of the population seems to) -- don't help overall. If you're using your bike for recreation but not utility, if you ride in a costume but not regular clothes, if you spent more on your bike than your teenager did on her used car; you're actively keeping bicycles out of the transportation mainstream.
Mainstreaming bicycling is what needs to happen most. It's a pipe dream to imagine that we'll hit 25% bicycle mode share in the States anytime soon, but the more we can encourage regular people to do regular people things on their regular people bikes, the sooner we'll see our fossil fuel-free bicycle utopia.
P.S. I'm not saying don't do epic rides or race or anything, just be aware that most people give zero shits about that and infinite shits about how to get to work/school.
P.P.S. I've always wanted to organize a series of grocery-getting rides. Maybe a cargo bike or two, but mostly just old Specialized Hard Rocks with racks and panniers, start two miles deep in a suburb, and ride to and from the nearest grocery store. Anyone have any experience doing something like that?