Yeah "serious cyclist" feels so impossible to define that it's meaningless. If I ride to work every day but go to a shop for maintenance instead of buying my own tools am I not serious?
Go to a shop to fix the problem, but have the basic tools and knowledge to make the temporary repairs needed to be able to ride the bike home or the shop.
Not really; a serious cyclist is someone who depends on and is invested in cycling as a mode of transport, who is not able to meet commitments if their bike breaks down without an real-time remedy.
So... no one within range of being able to catch a bus is a serious cyclist because they have an out? No one who can call a friend for a ride can be serious about cycling? I don't think this is typically what people would mean by that phrase.
Yes; if you go out thinking, "I don't have to care about the condition of my bike or what to do if it breaks down because there are bus routes along the way, or I can call a friend," then you're not a serious cyclist.
Using your logic, I must not be a serious driver because I don't drive with the equipment necessary to repair my car. Or my bike, when I am riding. Or my e-bike when I am riding that.
Folks who are serious about any hobby or activity are also often relentlessly practical. I used to ride 100km from the city I lived in, out to my brothers farm. It was not a particularly long or challenging ride, and it had cell service most of the way, even 20 years ago. I always did a gear check, and carried spare tires, but in 4 years of doing that 20-30 times per year, I replaced tires, but never a chain on that ride. I also never carried the tools to do that work because it fell into the category of unnecessary gear. If there was a problem, I was only about a 30 minute wait for help from either side if I needed to be picked up.
I also used to do a fair bit of trail riding, and for a much longer period of time, and for significantly technical trails. Again, a gear check ahead of time, and proper maintenance meant I took tubes, but not the chain repair tools (and one time I regretted not taking 4 tubes, because it was a long and hot 14km hike back carrying my bike on a July afternoon).
I am not going to gatekeep your ability to gatekeep, but you should at least understand that your perspective on what constitutes a "serious" cyclist is completely subjective and not rooted in anything meaningful.
Pretend instead of “serious” they said “frobnozz”. You’re not a frobnozz cyclist unless you can do a handstand on your handlebars! How absolutely un-frobnozz can you get??
There’s a tendency to ascribe value to words like “serious” but it’s a temptation, nothing more. Who cares that some bozo thinks “serious” drivers drive manual transmission cars, or ride bikes in a particular way.
I imagine serious cyclists also carry spare spokes, spare brake pads, spare derailleur hangers, spare bearings, spare cables, spare tyres, lubricant, assembly grease, spare batteries, spanner for truing bent components, hydraulic fluid (if using disc brakes), spare helmet in event of crash, etc.
The worst mechanical I ever had was a rear derailleur which deformed under load and pulled into wheel. I have never heard of anyone carrying a complete spare derailleur unless on a round the world trip.