AFAIR it was a problem almost a century ago, not now. It's still a thing I can't get comfortable with, but there is no chance of going wrong of a car just running while it's being fueled up.
Some fuel systems are pressurized these days, running cars with such a system opened up to the air will cause warnings to be displayed on the dash. Probably fine but may cause confusion/unneeded mechanic visits.
I personally will continue to religiously minimize spark and heat sources while fueling. I've seen damaged spark plugs complete their circuit by sparking through the air (and apparently keep running the engine just fine). Best to eliminate a class of problems entirely.
It's an engine and the brakes are friction. Parts of it get very hot. The whole thing is a huge heat source. Cars get hot enough to light dried grass on fire. The risk is inherent in the platform.
Outside of not fueling near an open flame, the more moderate strategy is to always plan your exits and know where that fire suppression button is relative to where you are.
Outside of not fueling near an open flame, the more moderate strategy is to always plan your exits and know where that fire suppression button is relative to where you are.
My car doesn't have a "fire suppression button", nor does my gas station, the closest they have is an emergency fuel cutoff switch that stops the pumps, but it doesn't do any active fire suppression.
Then your state almost certainly requires them to have extinguishers, or they have an automatically activating system. Not all states require an automatic system, but there is definitely fire specific equipment at the place where you are fueling your vehicle.
Familiarity with your surroundings is far more valuable than superstitious behavior.
In my state, there's no requirement for an automatic system, and no requirement for a fire extinguisher at the pumps, just that they have to have an approved 20BC extinguisher no more than 75 feet from the pumps.
My mother-in-law once attempted to turn on the ignition while my father-in-law was pumping gas. She was hot and wanted the A/C back on.
My wife and I were in the back seat and not pleased by that action. I would think a modern car can handle that without exploding but why risk it? Just deal with the heat for, oh, another 30 seconds. We were filling up a Honda Accord, not some camper van with a giant tank.
I personally will continue to religiously minimize spark and heat sources while fueling. I've seen damaged spark plugs complete their circuit by sparking through the air (and apparently keep running the engine just fine). Best to eliminate a class of problems entirely.