In my humble opinion, if you own a store and want to pick and choose who you serve as customers, then that is your right. You're the one paying the rent, overhead, bags, register receipt paper, electric, phone, hangers, display shelves, merchandise, employees, insurance, utilities, etc.
That sounds so logical, but then there are those who would use that right to discriminate, then it doesn't sound so logical at all. Anyone that owns a store is in it to make money, and being picky might lose you some customers, especially if the word gets around. And, there are laws to prohibit such, so an owner would have to be very careful.
Some places of business specify (with signs) that you are not allowed entry if you are barefoot, wearing a bathing suit, or eating, but I don't think you can specify "no Gays - Transgenders allowed", in the US that would be illegal.
When I had my shop, all were welcome. Until they showed they were not fit to be there under my business roof.
I guess if they are being disruptive or misbehaving, the owner always has the right to ask them to leave, but barring someone at the door might get a shop owner sued.