I think the First Amendment should be extended to say that NO ONE can attempt to limit anyone else's speech in any way (i.e. that every corporation, university, internet forum, social network, and anything else must have complete freedom of speech). With that said, no one would have to hire anyone who goes against the mission and beliefs of the company.
This idea is incongruous with the notion of property rights. If you own an establishment, it naturally falls upon you to define standards for appropriate conduct on your grounds. Not to mention that your stipulation of "in any way" would suggest no limitation on incitements to violence and threats to public safety (e.g. falsely yelling fire in a crowded theater), which are not protected by the First Amendment. Overall, I have to agree with this:
Legally allowed to? Yes.
Should we be indifferent to it and never complain about it? No.