If you ride a motorcycle, you're a motorcycle rider, if you drive a car, you're a driver. Drive any motorised wheeled vehicle, and you are a motorist. Ride a bicycle (or tricycle or whatever) and you are a cyclist.
If you do it all, you are all of it. It's an umbrella term.
If you hit someone not in or on a vehicle, you're hitting a pedestrian, regardless of whether that person stands still, jogs, sprint, doing yoga, or whatever.
Sometimes I'm a pedestrian, sometimes I am a passenger in or on some vehicle (wheeled or not), sometimes I'm a rower, sometimes I'm a cyclist, sometimes I'm a motorcyclist (one subset of "motorist") and sometimes I'm a car driver (another subset of "motorist").
Cyclist is an umbrella term, so, yes, I sometimes "identify" as such (when I'm on my bikes, mostly). However, there are many subsets of "cyclists", so whether one is commuting, another grocery getting, mountain biking, gravel riding, touring, bike packing, road biking, endurance riding, and a plethora of other subsets, you are still a cyclist. Doing one, more, or all of the different subsets doesn't mean you're not a cyclist.
Look at the laws everwhere. If you're riding a bike (not a moped or motorcycle), you're a cyclist. It is just a word meaning you're on a bicycle (or tricycle or unicycle or whatever).
There is nothing wrong about the term, it is not perjorative other than what some people want it to be when it suits them (context!). The only problem with it, as with all umbrella terms, is that it quickly becomes pretty vague and useless the moment you try to differentiate between different subsets.
Oh, and you ARE a motorist when you drive a car. It doesn't matter if you like driving it. You are still a motorist.