Comparing private residences to public venues makes sense in a particular and limited sort of "technically correct" way, but is rarely the basis of a persuasive argument.
Because it's generally open to the public. Different rules apply to your home and your grocery store even though they're both "privately owned". The law, and most people, recognize numerous differences between the two even if you do not.
If the owner of the venue personally stood in front of the entrance and recognized and denied entry to those lawyers, would that be illegal? What's the part you have an issue with, the automation or the banning?
First, we're not talking about simply legal vs illegal, there's also ethics and civics involved.
These venues are often publicly funded, supported by public services, are generally open to the public. So all such actions around banning members of the public for their identity (versus their behavior or conduct at the venue) should be given heightened scrutiny.
To your point, I do not agree that the venue should be able to ban someone simply for who they work for.
But the technology is what enabled the venue to identify and ban this lawyer, so it is a simply augmenting the scale of abuse by increasing the "hit rate" of recognition that the owner standing outside the venue wpuld.
It is a force multiplier of discrimination. And it reduces the cost of such discrimination significantly.
