How are you going to define that outside your preferred scenario of bigotry against gays? Do you intend to insist (by law) that Orthodox Jews, for example, work on Saturdays because that is more convenient for you and that that they are being intolerant of your beliefs for no rational reason?
What about Orthodox Jewish wedding photographer? Are they required to work for you on a Saturday or is it OK for them too refuse you service based on their religious beliefs?
It's ok for Jews to be Saturday-intolerant, just as many Christians are Sunday-intolerant. Days don't have feelings or human rights. And there's not a long history of discrimination and institutionalized biases against Saturday, the way there are against gays.
Monday, maybe, but definitely not Saturday.
In both cases the vendor is refusing to conduct business with the customer due to religious beliefs. Why do you think it is OK for the customer to have to find a new photographer in one case but not a different baker in the other?
I really have a hard time with the idea that the government is expected to pick the "right" set of beliefs to back on what should just be a voluntary transaction. Either both parties agree to conduct business or they don't. I realize that a laissez faire approach to commerce is not what we have today but I would prefer it over asking the government to mediate. And I do realize that would allow people and businesses to discriminate, but that just represents a business opportunity for someone else.
Is is always important to remember that "has a role" really means "can use force to ensure compliance".
Just think about the way modern media companies constantly shame and stigmatize people. How are you going to even define when someone is "shamed" or "stigmatized"? Aren't there people who should be shamed and stigmatized?
This seems completely unworkable and guaranteed to make absolutely no one happy other than the lawyers making money off of all the frivolous legal disputes.