Which government would come after them? There are lots of different governments around the world, with different views and different laws.
> How is refusing to serve legal sex workers different?
As far as I can tell, in the US discrimination is forbidden against certain protected groups / along certain protected differences only. But you are free to discriminate on all other grounds. Eg a restaurant can legally discriminate against people who don't wear a tie.
In the British rules, sexual orientation is explicitly mentioned, but your trade ain't. So as far as I can tell, it's illegal in the UK to discriminate against gays but legal to discriminate against sex workers.
(However, a government might come after you, if you do something they don't like, even if it's perfectly legal. Eg the government could just 'randomly' decide to audit your taxes all the time, or 'randomly' apply other regulations and rules more strictly.)
I understand and am sort of aware of the laws. It seems however very hypocritical to discriminate base upon profession. IANAL but I suspect that if for example airline will not let passenger to board a plane citing that they work "shitty low paying job" as a reason said airline might get in trouble anyways.
I think the Soviet Union, Nazi Germany, Iran since the Islamic Revolution etc went for a less legalistic and more moralistic approach.
(Of course, you should still evaluate these policies on their own merit, instead of tarring them guilty by association. To give a counter-example: Nazi Germany was one of the first places to put anti-animal cruelty laws on the books and officials were very concerned about the dangers of smoking. Two stances that are widely popular today, and rightly so.)