We are all cyclists. I know what the OP has in mind, but we are all people on bicycles; we are thus all cyclists.
I often wear lycra, but not always.
I am an enthusiastic driver and I adore cars. I love motorcycles too, but no longer ride one.
I used to drive a lorry and was a cyclist even when I did that.
I do not get angry about mobile-phone use, helmets, HGVs, cycle lanes, shared-use paths....
I do not own any team kit and do not dream of electronic gearchanges.
I have a fixie with DIY bullhorns, but am too old and fat to be a fakenger or a hipster.
I rarely wear a helmet, but I love to wind up riders and non-riders on both sides of the debate who take the whole helmet thing terribly seriously.
I haven't undergone training since childhood and would never seriously be able to state that I am a 'cycling advocate' or some such other silliness.
I see the roads as one big happy family of road users, with the occasional blast of road rage from a driver or strange, shouty lecture on road tax from a cyclist with no perception of how much of a fool he looks and sounds.
One or more of those statements may make me anything but a cyclist in the eyes of some, but I'm happy to bimble along and keep enjoying it.