I’m putting the moral issue aside for the moment, and discussing the legal context for employment, under U.S. law.
Discrimination based on race, religion, national origin, ethnicity, gender, age (over age 40), or disability is prohibited, under Title VII of the Civil Rights Act of 1964, Age Discrimination Act (1967), Americans with Disabilities (1990), Equal Pay Act of 1963, and various others.
There are exceptions permitted under the law. These main exception is a bona fide occupational qualification (“BFOQ” in the jargon). Thus, if you are casting a movie and want someone to play George Washington, you may justifiably exclude a black woman actress who applies… even if she is a better actress than the white male you select. Your example of hiring for a basketball team would be similar, you can prove that height is a relevant qualification. If you wanted to hire a rabbi for a congregation, Izzy, you would NOT have to accept Catholic applicants.
Other exceptions include seniority systems, national security, and a few others. The courts have interpreted these very strictly.
The situation with persons with disabilities is complex, but you basically can’t discriminate if they can perform the essential job functions, perhaps with accomodation.
Saying that you want to hire primarily Mexicans and therefore are discriminating “in favor” of a group, not against a group, is a ludicrous argument. Suppose I want to hire primarily whites. It’s discriminating against all other groups.
Now, it is not enough to claim that you do not discriminate in hiring, but you “just happen” to have excluded some ethnicities or races. It is called disparate impact, and it is also prohibited. The prime example is an employer who only hires people who live within a 10 or 15 minute drive from the office, and happens to be located in a white neighborhood and thus has no black employees. There is no specific exclusion of blacks in the hiring practice, but the geographic restriction creates “disparate impact”. In this case, the courts have ruled that the employer cannot specify driving time to work as a condition for hiring (unless it can be proved that it is a bona fide occupational qualification.)
In short, g8rguy, if your workforce turns out to be “composed entirely of lesbian atheists from Venezuala”, then you better be prepared to prove that there is not discriminatory practice going on when a well qualified Catholic male from Hindustan sues on the grounds of disparate impact.
Your defense against such a suit cannot be “it just happened that way.” Well, OK, you can try such a defense, but you will almost certainly lose the case. You would have to prove that there was absolutely no bias in your hiring, that on some objective measure you ALWAYS picked the most qualified candidate withour regard for race, gender,e tc. No jury will believe that by sheer dumb luck, you just happened to wind up with 100 employees who are all “lesbian atheists from Venezuala.”
Your primary defense against such a suit would have to be to show that being a lesbian atheist from Venezuela was a bona fide job qualitifcatin. Good luck.