I can see no reason why there isn't room for both in our lives.
At various points in the year I'll be in various cockpits, jeans and a jumper at my microlight club in the backroom of a pub, in overalls on my back under an aeroplane older than me in a hangar older than my Dad, putting on a suit to meet with people that control power and money, and in black tie at a formal dinner of something like SETP or RAeS. I'm good with all of the above, just need to use the nailbrush quite a lot if I'm doing both dirty and clean the same day.
I've sat at black tie aviation occasions next to people whose "hands dirty" exploits probably put what any of us have achieved in our lives look pretty bloody tame - whether that's flying combat, flying into space, or just plain doing something the rest of us could never dream of (I recall once a friend, who used to be Chief Test Pilot for NASA, coming up to me gleefully and explaining that he'd just filled up an aeroplane for the first time - and this is somebody who Test Flew SR71s: just proves that everybody has missed out on something in aviation.)
On the whole, the only people I have an issue are either the efete wastes of space who believe that getting their hands dirty is beneath them, or the inverted snobs who believe that because they spend most of their time in overalls that there's something wrong with occasionally dressing up a bit, meeting with other high achievers, and enjoying good food and company in a smart environment.
G