The analogy you made in this video about a circle of friends seems like a false comparison to me. Choosing friends is a matter of personal preference, and you're right that the government should not impose standards on that sort of thing.

However, which customers you choose to serve is different. The woman you interview mentions that she chooses friends that are similar to her, ones that don't cause drama, and you say that business owners should have a similar ability to choose customers. But when you open a business, you are not bringing people into your life as friends, you are interacting with them professionally, in an exchange of goods or services for money. If a customer can pay and is following the law (e.g. not causing public disturbances at your establishment) then there is no reason to turn them away. It doesn't matter if their lifestyle or identity is "against your religion", or if you think they're unworthy of your services for some other reason, because you're not being forced to live in those ways--only to serve a fellow human being and treat them with dignity and respect, despite differences in belief or lifestyle.

If a business owner can't separate personal belief (or in some cases, bigotry) from the way they conduct their business, they probably shouldn't be conducting a business.