Barry Goldwater made the argument that Title II was unconstitutional.
And I have to say that I found his argument pretty persuasive. However, the SCOTUS disagreed. And I think it may have been unanimous.
Thing is: anybody who makes this argument today is basically cast as a defender of segregated public facilities (water fountains, hotels, restaurants, etc).
We sometimes have a hard time distinguishing between an argument which says “people should be free to do X” and “people should do X”….with almost everything other than abortion, anyway.
Here’s a speech where Goldwater explained his opposition to Titles II and VII, which caused him to vote against the CRA of 1964.
Again, I think a lot of people (probably most people) today would confuse this for an argument in favor of segregated public accommodations. And that’s because the virtue of principle and the proper scope of federal governance have gone out of style.