My wife does not like to fill the vehicle up with fuel.
But I would not equate that as anxiety.... It's just something she does not like to do....if we are together, I'll fill it up, sometimes she asks me to take her car and put gas in it. If she needs gas and I am not around, she fills it herself.
Again, no anxiety....I think it's the smell of gasoline, and not wanting to get any in her.