Regularly watching cyclists flaunt the rules that the car driver would be cited for breaking, and never seeing a single cyclist cited for the law breaking, leaves a foul taste for cyclists in the mouths of many motorists. They don't get to run stops or red lights with impunity and without punishment.
So as long as the law says cyclists must obey the same rules car drivers are also supposed to obey, the subset of cyclists that break those rules on a regular basis do not help, in the least, the arguments to try to convince car drivers to be more respectful of cyclists.
The start should be the cyclists obeying the same rules as the cars (which would help with not pissing off numerous car drivers daily) while working the politician angle to change the rules for cyclists to something safer for cyclists (and at which point the car drivers will no longer have a way to rationalize their hatred of the cyclists as just "law breakers").