Is it permitted to not take Ph.D. students who have girlfriends/are married/don't come in weekends...? As a professor, are you permitted to prohibit Ph.D. students from joining your research group if you know they have a boy/girlfriend, are married, don't come in on weekends, who don't stay late, etc...?

The professor does not intend to make them work on stuff related to his/her research outside of normal working hours.  Rather, the supervisor would like their students to be driven enough to study/read publications and books about topics outside their particular research program during those times.

That way, supposedly, by the time they graduate, they will be very well rounded, and also develop their own research programs in meaningful ways.

Since I observe this behavior with a certain professor I know at a US university, I was wondering if that professor is liable for legal charges, which I could bring up to the dean.

One way I hear about how he "weeds" out the normal people is by telling them how much work it takes to succeed, and gives examples of previous "successful" students, and what their lifestyles were. I suppose he says something like: "this is how much you know from being an undergrad, this is how much you need to know to succeed in this field, here is a humongous list of topics you should know before you can competently do research with me, come back to me when you're ready." But I don't think that's all he does....  I think he intimidates prospective advisees with his demeanor, and so this fact along with his reputation leads to him select students who work day and night everyday.
A disclaimer:  I'm not an attorney.  My opinion is my own but I'll give you my sources.

Here in the US only, universities are probably not prohibited from considering otherwise protected status in admissions, c.f., Fisher v. University of Texas at Austin, which upheld racial preferences in admissions.

But under Title VII of the Civil Rights Act of 1964, as amended, once the question becomes one of employment (e.g., they work for you and get paid a stipend) you cannot discriminate based on any of the factors you cite.  You should also carefully avoid asking questions that suggest you're even thinking about it, c.f., "Federal Laws Prohibiting Job Discrimination Questions And Answers" and "Pre-Employment Inquiries and Marital Status or Number of Children" on the EEOC site.

Added: I agree with Anonymous. Even if you think you can get away with it, perhaps because it's not illegal in your country, I also think it would still be wrong.

Added:  If you are the victim of unlawful discrimination in the workplace, HR is not your friend. A priori, their objective is to make sure discrimination complaints don't happen. But after the fact, their objective is to circle the wagons and make sure a complaint dies without the institution having to pay a settlement or admit that any wrongdoing has ever happened.  A great outcome for HR is that you just quit and the problem goes away.  From your latest performance reviews and interviews with your co-workers, it's clear you were unhappy and have been for months and it's been showing up in your work.  So you quit.  Poof!  Problem solved.  Separately, they'll figure out what to do with the others involved.  If you think you may be a victim of unlawful discrimination, you should go first to your own attorney for competent legal advice, not HR.