On or off doesn't matter to the car at all during fueling.
The prohibition is to help prevent some human caused fire issues, namely generating static charge (sparks) by getting in and out of the car. You can proactively discharge the static harmlessly by touching the car's metal before you grab the fuel dispenser to remove it.
MajorFrantic t1_ixt40gv wrote
Reply to ELI5: Why do you have to turn your car off when you fill up your tank? by logan0921
On or off doesn't matter to the car at all during fueling.
The prohibition is to help prevent some human caused fire issues, namely generating static charge (sparks) by getting in and out of the car. You can proactively discharge the static harmlessly by touching the car's metal before you grab the fuel dispenser to remove it.