In your examples, the answer to the pharmacist question is yes. A pharmacist is allowed to refuse on moral grounds as long as you're able to fill it elsewhere (and they must allow you to have the prescription back if you've given it to them already and they don't fill it)... which means that as long as any pharmacy exists anywhere, they can technically refuse and it's not discrimination.
I think "right" is a tough word to use here. Some forms of discrimination may be no more than poor business decisions- not taking business from, say, purple people because you don't like purple people. Those are private businesses. So really, the private business owners, as bigotted as they are, are only screwing themselves out of money, but I don't think any actual law is being broken (as I understand it).
Public services and accomodations, however, and stuff run/paid for by the government, are definitely open to everyone, and there would be no place for discrimination.
My EMT professor put it very bluntly to my class, when the subject of discrimination came up at the beginning of the semester. She said if anyone had any sort of bias or discriminatory feelings towards any kind of people, we'd better either leave the business, or get rid of it immediately. Because, "when you're standing over a patient who needs your help... no matter what color, religion, or sexual orientation they may be- we all bleed red."
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