So I can go to a muslim bakery and demand they make me a bangers and mash cake (bangers has pork in it), or a mohammed cake?
Nope.
If the Muslim store refuses to sell pork
to all of its customers, then they don't have to sell it to you. If they refuse to make cakes in the likeness of Mohammed to
everyone who asks, then they can refuse to do so for you.
What the store cannot do -- and yes, this has been litigated -- is sell bacon to some people, but not others, on the basis of religion. Or, make Mohammed cakes for some customers, but not others, on the basis of religion.
How many other bakeries would be happy to bake them a cake?
1963 called, and wants its anti-civil rights arguments back
If you let one business discriminate, then you can't stop another business from discriminating. In short order, huge swaths of the US will deny services to people based on race, creed, gender and more.
Do people have a right to religious freedom, freedom of association, and freedom to conduct business or do they not?
Not when they are operating as a public accommodation.
If you agree to open your doors to the public, then you do not get to decide who is and is not a member of "the public." You have an obligation to treat all customers the same, regardless of race, creed, gender, and in some states sexual orientation.
Freedom of religion, and freedom of association, is protected by allowing private organizations to discriminate as much as they want. But if you want to associate with the public, again, you do not get to decide who is and is not a member of "the public." Nor does the freedom of religion empower you to discriminate against members of the public; you have to do that in private.
And FYI, millions of segregationists
did try to justify their racism by citing religious beliefs.