Not the same issue. Bakeries were, and are, free to refuse to make a cake based on the message conveyed by the cake. You can't demand that a bakery make you a cake in the shape of a dick, nor can you demand they make you a cake with a swastika on it. What got these bakeries into trouble wasn't the nature of the cake itself, but the fact that they didn't like the
people who asked them to bake it. And, frankly, fuck them for refusing. You're a baker. Do your damn job.
With Yaniv, the waxers are in fact doing their damn jobs, which is to wax ladyparts,
not balls. Anyone who's ever handled both male and female genitalia doesn't need to have it explained to them that waxing techniques designed for vulvas may not be well suited to safely handle the paper-thin skin of the scrotum. It's not the same job.
This is not even remotely true. Businesses were perfectly free to serve an integrated clientele if they wished; that's what the
Negro Motorist Green Book was all about. But many or most prominent businesses--e.g., the lunch counter at Woolworth's--chose segregation or whites-only instead, leading to widespread denial of civil rights.