That’s a very different situation compared to the standard “sign up with your email here”. The provider is responsible because they picked their clients, rather than their clients picking them.
If the bartender decides as a rule "first of all, if they seem uncertain on their legs it is already a no", again that is just a codification of the former.
Nobody in the world DOES NOT do this. If an advertiser takes down their ads from a website because that website is spreading white supremacy then they are doing just the same. As they should.
Also where do they claim they are "just an infrastructure provider"? They clearly say throughout that they provide services for anti-racist/anti-sexist/etc orgs that can't afford to do it themselves.
They do not make a profit. They are not a company. They are literally a group of friends helping orgs out.