In the old days lefties wrote with their right hands just fine - they were forced to.
I'm left-handed and I use scissors with my right hand just fine, and the same goes for my computer mouse - I don't want people switching it every single time they want to use my PC. And I never cared about left-handed scissors. The car shifter doesn't really require high dexterity, unless you have a very old car, I guess; I wouldn't know.
If someone is left-handed nowadays, chances are they can use most tools with the right hand, too - and in the past, they were trained to be right-handed. So the difference would be only slightly significant in cooperative activities(maybe a more suave learning curve, but that's it - and that's enough to condemn your future in football, I guess). In a competitive sport, however, being left-handed is a big edge - you trained all your life against right-handed people, but they aren't as prepared for you.
Sports only brings the more dramatic results, I think.