or do what they want as it's their website

bad argument. we dont let bakers discrimate against gay people. being a private business, doesnt mean you can do whatever you want.

Edit: I agree with the posters below me. My point is a private business doesnt mean I can do whatever I want. There are still social rules and laws that need to be considered.

Because gay people face systemic societal discrimination, so we have made them a legally protected class. Private businesses are free to ban or censor whoever they want as long as they aren't targeting a protected class.

Bakers can discriminate against you for your political beliefs. Political party affiliation is not a protected class.