My gut reaction is to say, "No, of course not." Then I step back and think for a moment, and I come up with "Why not? Why should the company be forced to hire, fire, not hire, or not fire anyone in particular?" The law already regulates sexual and racial discrimination, among others, but how about viewpoint discrimination? And don't throw the First Amendment at me; it applies to government, not to private companies.
Not too long ago I read about a company that didn't want to pay such high premiums for employees' health insurance, so it required employees to stop smoking. Not just on the job, mind you, but stop smoking! Is that right? Should it be legal? Those are two very different questions.
Usually in such cases I come down on the side of the employer. The case in this article, though, is intriguing. I'm still inclined to agree that the employer can and should be able to make this decision, but that it's a stupid decision to make that may (hopefully) cost them.