You are a good person. You are tolerant of many viewpoints and you want a diverse team that is reflective of your clients and the community you work within. You know it only makes your team stronger.
But when you are hiring, your senior obligation is not to round out your team, it is to hire the most qualified person you can find, regardless of their background. You may have the desire to add someone with a certain kind of background or credential to your team ("we need an MBA around here"). Or perhaps your organization has too many men, or women or whatever. Of course your candidate sourcing and recruiting efforts should make every effort to draw from a diverse candidate pool--anything less is stupid and short-sighted. But when it comes time to interview, after you've done your level-best to recruit wisely, your obligation is to consider every single qualified person.
It's a mistake to allow hiring managers to cherry-pick resumes, only interviewing the people who meet certain criteria unrelated to job performance. Too many hiring managers forget the real priority in hiring. It's hard enough to hire great people, and when you artificially limit your candidate pool (to consider only people with an MBA for example), you've done your organization a real disservice.
You owe it to all your other employees to hire the most qualified person--everyone's livelihood depends on it. Before you make a hiring decision, take a few hours to be sure you have interviewed all the best candidates. By doing this, you will understand exactly what you are giving up when you insist on any hiring criteria that is unrelated to job performance.