People being rude are common enough that, if shops decided not to serve them, it would leave a lot of people without suppliers, probably the large majority of customers, actually (not to say that people are mostly rude, but most people can be rude sometimes when they have a bad day). It could also push quite a few businesses (those who can't afford to lose any customer) to fail, while others would be able to survive (because they make enough profits to select their customers).
So, naturally, a business-savvy person would open a shop targetting specifically at this mass of customers with money & need to buy things and nowhere to buy, saying "my motto will be customers is always right". And they would hire employees, knowing full well they'll have to interact with these rude customers. Logically, they'd need to pay more for their workforce (since presumably, employees would accept a lower wages to work in "employees-first" shops, and look for jobs in "customers-first" shops only if they can't get a job in the former), but they would fill the vacuum anyway, unless the wage differential is so great that they'd lose money overall.
Barring a strong aversion from the workforce to work in such environment (and demanding very high wage for doing that), any significant attempt by shops to select their customers would result in a return to the current situation after some time.
Morrus said:
The latter (usually, not always; if you're buying limited or exclusive product it magically reverses; gosh, why? Try buying a new Rolex and see how far 'Karen' gets you) is more like a reasonable dynamic between two people exchanging goods/services.
High-end shops are doing "the customers is always right" better than most, but not in the sense you're thinking.
The customer being always right thing doesn't necessarily mean one has to be rude. It's taking care of the need of the customers. Let's take an example in the middle-range shops (not Rolex-level): for some unfathomable reason, an hotel where I am often staying at for work isn't having roasted potatoes at the breakfast buffet in their executive lounge, despite potatoes being available in the main restaurant. I enjoy roasted potatoes for breakfast, and I politely conveyed my distress about this situation, to the staff and to the satisfaction survey. As the result, when I get breakfast there now, they send someone to the main restaurant to fetch roasted potatoes for me. That's the meaning of "the customer is always right": if I want potatoes, they should endeavour to serve me potatoes. Contrast to the number of places where filling in satisfaction survey doesn't prompt any change down the line! The price of the product entails a margin for entertaining the common whims of the customers (in this case, quite easy to satisfy), and their desire should be satisfied. Possibly by offering them to pay for something out of the ordinary: if I wanted to have champagne each morning, the correct answer would be "sure, we can get you champagne for € XX at breakfast" (the customer is always right) and not "we don't care about what you want, there is only coffee and OJ at breakfast" (the customer is wrong, noone should be having champagne for breakfast). The former attracts loyalty, the latter makes the client look elsewhere for a place where they'll accept to sell him the champagne he wants.
EDIT: To get back to Rolex-type shops, you can afford to be a Karen much more as a customer (and again, without needing to be rude about it, because you get what you want without having to "speak with the manager"). If you want to try a suit, and get to an off-the-hook store, you'll have to move to the store, try the outfit, and be happy with it. Most Savile Row tailors, on the other hand, will accomodate you if you want your measures taken in the comfort of your own home or office, get back to you for trying it out at the time and place of your choice, and not require you to lose your time visiting their shop. They practice "the customer is always right", and it's part of the reason people still buy bespoke suits instead of getting mass-market clothings, which are generally much more affordable.
I guess the whole Karen situation is occurring more because shops say "no" instead of "sure, we want you to be our customer, here is the price tag" -- which would shut most Karens up, since they'd get an offer to get what they want, and can decide whether to go through with the deal.