Why would that argument not apply to "It's 1960, and I don't want to seat black customers at my fancy restaurant because it's statistically likely to be less profitable than seating white customers"?
Why? Servers claim that black customers - on average - tip less.
I don't know how prevalent this belief on the part of servers is. And I don't know how much of a numerically accurate basis in reality it has.
But, as a thought experiment, imagine for a moment that there exists an identifiable group [black people, star trek fans, old people, dentists, ...] that are likely to lead a server to go home with less money at the end of the night.
There can be a really fine line between statistics/machine learning and "bias"/"racism".
Where it gets even more complicated is that there might be variables which are not expressed as "is the customer black" which ultimately predict/are highly correlated with the question "is the customer black" - but are also predictive of the question "is the customer profitable".
There's no line. Learning and bias are the same thing.
And that's the way we treated this in the 1960s. The government didn't ask Woolworth whether they had legitimate economic reason to refuse to seat those black college students, or whether their objection was based on them being college students, or because they only ordered coffee and not a meal, or anything else. As long as the effect of your policy was that you were discriminating on race, it became illegal. It doesn't matter whether you had valid reasoning based on race and economic status being correlated, or you were a card-carrying Klansman. A good-faith policy that discriminated on race is still illegal.
It seemed to work pretty well, and I don't think many of us regret the loss of ability of restaurateurs to make these particular economic decisions. The fact that we can now offload these decisions to algorithms (which aren't likely to be "racist" in the conventional sense) instead of humans shouldn't change things.
It's probably worth pointing out that the restaurateurs didn't have the ability to make those decisions; that was the point of the Jim Crow legal regime. Left to themselves, they kept wanting to serve blacks.
If you have more customers trying to make reservations than tables to seat them, it is economically rational to seat the customers most likely to buy your more expensive items. We decided (correctly, IMO) that it is more important for society to fight entrenched racism than to enable business owners to make that particular locally-rational economic decision.