I think statistics should be expressed as percentage of miles travelled or as a percentage of road users. There are more accidents with cars , but there are are a lot more cars.
I may assume the hate for "lycra" cyclists comes 1) from sport enthusiasts in country road that ride side by side or in packs, causing a more problematic overtake and sudden braking to 20mph if on the other side there is no incoming traffic.
The great majority of lycra cyclist will immediately stay on the side of the road, no more riding next to each other to allow cars to overtake.
It is the few ignorant that continue side by side holding a car up that infuriate the motorists. You tend to remember this 10% of idiots, not the 90% of well behaving "lycrist".
2) lycra in town commuters and bike deliveries. Not all, but many, many, adhere to no traffic rules. Red lights, pedestrian paths, cutting in front, you name it. It's not all the cyclist, but this portion of commuters or delivery people that respect no rules infuriates other motorists and are indeed a danger to pedesteian and an annoyance to motorists.
Again the tendency is to erroneously label all "lycrists" as idiots riders, but that's a stereotyping that is unfair to the many law abiding and respectful ones.
Of course you can find the same difference within motorcyclists, car drivers, bus drivers, or even people walking for that matter