No, no, no. A person running a business DOES NOT have a right to choose who he will serve. That right, which may have existed previously, was abrogated with the Civil Rights Act of 1964, which makes it illegal to refuse service to someone based on "race, color, religion, sex or national origin".
There is also the issue of property rights. People have the right to control their property whether it be bake shops and ovens or paint brushes.
Again, no. Under the same law it is, for instance, illegal to refuse to sell your house to a black person because they are black. It's illegal for a group of people to get together and say "this is a white neighborhood and no blacks can move in here".
This has been the law since 1964 in the USA, so 54 years and counting.
Not many conservatives or Christians will dare stand up for these fundamental rights.
You describe property rights, and the right to discriminate as fundamental, but the Civil Rights Act is pretty fundamental too.
There is no call for repealing it, or any part of it.
The last politician I am aware of who pointed out that by granting the civil rights cited above that certain other civil rights (the ones you consider "fundamental") were being reduced or abrogated was Rand Paul in a long-form interview with Rachel Maddow. She got him to admit his ambivalence towards the 1964 Civil Rights Act's "public accommodation" clauses. It was not a good look for Rand, and he spent about a month backtracking before he put it behind him. (1)
The issue was raised at the time the act was being debated. If you read Sen. Goldwater's campaign book "The Conscience of a Conservative" he goes after the issue hammer and tong. (Brett Bozell Sr. was the actual writer, apparently). So the issue had a full hearing, and even in 1964 people decided that the right not to be discriminated against in public accommodations was more important than the absolute property right to refuse service based on whatever consideration.(2)(3)
I don't think that there is much of a constituency to go back and re-litigate this, or that there are very many people supporting the "property rights above all" position. Those who do are usually Libertarians or even Anarcho-Capitalists, who view property rights as the most important (fundamental) rights of all. Perhaps you are one of them? Regardless of your personal beliefs, I agree with your sentiment that there is no push by most Conservatives to install property rights (back) on their throne. Only a small fringe minority of people on the Right, and virtually no one on the Left, take this position. .(4)
Good luck with trying to defend the right to practice one’s religion when all the other rights have been denied.
The practice of religion is bounded by law in America. It is not an unlimited right that trumps all others, in all cases, every time.
Christian Scientists are not free to deny treatment to their children, Rastafarians are not free to smoke dope (in most states, still), Moslems and Mormons are not permitted to legally marry 4 woman in the USA.
Some theorists on the Alt-Right would like to re-litigate this. They feel if the previous regime of lassie-faire free-association can be re-instituted that de-facto "ethno-states" (sometimes referred to as "PLEs" or Private Little Europes") can be created in the USA. Alt-Right leader Richard Spencer no doubt considers sacred property rights an important tool in the process he has described as "non-violent ethnic cleansing" which he advocates.
NOTES:
1. Rand Paul steps in it with Rachel Maddow. HERE.
2. Electoral College, 1964. Red States voted for the guy who wanted to support Property Rights over Anti-Discrimination Rights.
3.Barry Goldwater: Conscience of a Conservative (Full book, PDF format.)
4. Wikipedia article on Anarcho-Capitalism.