must a butcher who sells regular meat provide kosher or halaal meat to those 'different' customers....?
No. Public Accommodation laws do not mandate what goods and services a business offers.
Public Accommodation laws require that if such goods and sevices were offerred (kosher or halall meets) then those goods and services cannot be denied based on the race, religion, national origin, sex, and in some states sexual orientation of the customer.
If the butcher doesn't stock kosher or halaal meets, they don't have to sell them to anyone. However if they do sell them, they cannot refuse to sell them to - say - an Chinese person because they are Chinese.
if he doesn't does that mean he is 'denying service to an immutable trait of his customer'......?
A trait doesn't have to be "immutable" to be valid under State Public Accommodation laws. Religion is not an "immutable" characteristic. Illinois, as an example, also lists veterans status (a non-immutable trait). Oregon, as an example, also lists marital status (a non-immutable trait) under it's PA laws.
See note above, since they are not required to sell kosher or halaal meets - your question is moot.
is the butcher 'denying freedom' to those Jewish and Muslim shoppers....?
No see first note, since they are not required to sell kosher or halaal meets - your question is moot.
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Right. PA laws don't actually require that a business owner treat everyone equally, or fairly. Or even that they don't discriminate. What PA laws ban is making a political statement via business choices. A baker, for example, can refuse to bake a cake for a gay wedding for any number of arbitrary, even nonsensical reasons, but if they do it as expression of their disapproval of gay weddings, the law steps in to silence them.
These laws specifically target opinions that the government wants to suppress. It's hard to believe the Court can't see that this is a violation of the spirit, and letter, of the First Amendment.