Cycling is environmentally friendly, but let's not equate world championship to cycling as transport. The event itself must have a lot carbon footprint. Still, weird choice of event to protest, but I can see them doing what they can to get the publicity they need.
And if they protested people commuting into a city, a huge source of global emissions, they'd be criticized for that too. People always manage to label protests as the wrong time/place. What they really mean is "protest is fine as long as no one, especially me, is asked to actually pay attention to it."
This is mildly infuriating but ruining the climate is very infuriating. So I understand the protesting and I hope we're gonna see a good second half of the race.
I don't know about this Cycling competition, but the Tour de france thing has more helper cars, truck, cameraman motorcycle. Entire mobile village with caravan, trucks etc. Thats a lot of ecological impact even if indeed Cycling is one of the greenest transportation method.
I don't know the ideologies of the protestors, but I do agree with protesting against "big cycling". Cycling around on a trusty steel bike which you can repair yourself is environmentally friendly. Buying a new carbon fiber bike every few years because it is 2% more aero than the last is not. Instead of standardized parts, the cycling industry wants you to buy cheap ones that break fast, and can only be replaced with their specific parts. They sell this to you by including some upgrades in chains, cassettes etc. The cycling industry is the same as any other industry, it exists to make profits. Truly sustainable things do not come from making profits.
My guess is that those "protesters" are paid and organized by some oil industry people (maybe without the activists glued to the floor knowing about this), just to give real climate activists a bad image. I've talked to a real climate activist recently, and she was furious about those "gullible idiots".
Cycling races are very polluting. Not because of the bikes but because of everything besides the bikes (cars, motocycles, cameras, plastic goodies, ...)