And when this is the case, we call those businesses "discriminatory" and either expect they do it in their own private circle or or figure out a way to serve everyone and run into as few issues as they may.
You may have the expectation, but I do not. I am not quite as intensely interested in controlling the actions of other people via government force as you are.
Sure, it makes it hard for a public business to cater to hardline bigots, but so what?
So, you could just let people associate as they please, whether you believe they are 'bigots' or not.
Do you seriously find that kind of world where, if you want to find a cabin in the woods surrounded by other cabins in the woods where only people of a specific appearance will be seen, you have to join a private club rather than just book a travel agent "hellish"?
I don't know where 'cabin in the woods' came from. What are you talking about?
I think that putting a facade of 'you can do it if it's a private club' is a ridiculous and time-wasting engineered loophole to patch a problem you created.
Let's say I want to open a male-only sex-on-premises venue, entry is $20. (I know homosexuality makes you shudder with disgust but hear me out). Under your 'no discrimination' regime, I can't. I can't stick someone on the door to vet who comes in, and I can't advertise in a way to discourage non-males from coming in, because that would be 'discriminatory'. In fact, the business itself can't exist because it is premised on excluding non-males.
So, instead, I form a 'private club'. Membership lasts for 24 hours. Because this is a private club, we can discriminate, and we only let people sign on to be members for 24 hours (24 hour membership cost, $20). You can sign on to the private club at the door, if the bouncer likes your look.
Now, either you can see the second scenario is just as discriminatory as the first, but requires ludicrous bureaucratic nonsense to survive because otherwise it would be "discrimination". It's like Islamic banking: you can't take out a loan with interest to buy a house....so you happen to be able to get around Allah's (peace be upon her) rules by buying the house (on a thirty year repayment plan) at the sale price plus what about thirty years of interest would cost....but we're not charging interest!
Or: an alternative scenario. Say I want to run an atheist-only dating service. Or perhaps a Jewish-only dating service. Or a Muslim-only dating service. This would appeal to people to whom the religion of a dating partner is important, specifically that it be the same as their own. Obviously, it would be discrimination to exclude the people who don't fit into the category, but it would be better for everyone who wants to sign on to such a service.
But so what if it is 'discrimination'? You think that by merely stating that, that makes whatever it is bad and wrong. It doesn't.