I think some of the respondants to this thread just don't get it.
First, there's the practical side to consider: the All England Lawn Tennis Club (AELTC), Wimbledon, London SW19, is a private tennis club. The "predominantly white" uniform rule is a strict rule that shows respect for the institution and the history of the sport. This rule is in effect for all who play at the Club during all days of the year, not just during the Champoinships fortnight. If you don't abide by the dress rules (which have been made more lax in the last two decades, by the way), you won't play there. Simple as that. When an infraction is noticed, the Club Chairman is dispatched to ask the offender to change, out of respect for the club rules. In a few instances, ignorant (or slightly rebellious) pros have had to change during the Championships, and they did - because they all have to admit that Wimbledon is special. It's the pinnacle of the sport, the most prestigious and historic of all tennis tournaments in the world. Even setting foot on the club grounds is special - so imagine finding yourself in the main draw for the Championships! Only 128 play in each singles draw. The tournament doesn't owe anyone anything.
Historically, we've seen some talented players skip the Championships because they may have thought they were bigger than the Championships. The early "Image is Everything" Agassi sticks out in this regard as an immature guy who didn't want to take part. He later matured and admittted his attitude in those early years was wrong.
The generally immature can be forgiven for thinking anything not "cutting edge" or "extreme" or "progressive" is bad. But these "archaic" institutions and events serve a purpose - they help us understand how we fit into history and how we stack up against the character and resolve of those who have gone before us. Hopefully none of our generations will ever be remembered as the "Generation Who Gave The Finger to History." Very shortsighted. Very selfish, too.
FWIW, in the mid-1980s, I spent summers in London, actually living about 3 miles from Wimbledon (in SW14), playing junior tournaments. Everyone dreamt of playing at Wimbledon, and for the most part, the clubs we played tournaments in all over England had a "predominantly white attire" rule. No big deal. Later in life, I would notice at the best restaurants, I couldn't get in without a suit and tie on! Unfair? No, that was merely part of the price of admission, and served not as a tool of the elitist, so much as a tangible way to show respect for the other patrons and the atmosphere of the restaurant. I would sometimes later eat in other establishments for a nice meal, where a guy would come in wearing sweats and a T-shirt, or something like that, and wreck the ambience. He may as well have been at McDonald's. Point is, to extend the analogy, Wimbledon isn't McDonald's. It's Dinner at the White House, The Vatican, Buckingham Palace, and Casino Royale, all rolled into one.