It's not utterly irrational at all. Slightly perhaps, and many worry about it where perhaps it won't really affect them but to dismiss it as utterly irrational is unfair.
I think we're going to have to disagree on this. How is it rational to not buy something on the grounds that it might not make it to the next refuelling location?
Is an EV showing 50 miles range to empty any different to an ICE car? I don't see it. And even if you allow for the longer refuelling times, that's not range anxiety, that's just bad planning.
You definitely have to change the way you drive. When I was younger I would drive for 6-7 hours and empty the tank on the car in one hit. I would buy cars on teh basis that they had 90 or 100l fuel tanks so I could drive to the far side of Germany without filling up. But as I've got older I need to stop every 2-3 hours and realistically that's about 200-250 miles of driving in an EV. So you stop for 50 minutes and you can go again for 200-250 miles. It's definitely slower, and any savings I make on fuel costs are frittered away on coffee but it's nothing to be anxious about. Just different.