The Supreme Court search process should be inclusive, not exclusive. Although the role of a judge is apolitical, the process of selecting a nominee to the Supreme Court is a political process in which factors other than qualifications inevitably play a role.
In searching for a Supreme Court nominee, a president should cast a wide net, considering qualified candidates from all walks of life. But, in so doing, a president must not exclude from consideration candidates with certain demographic profiles.
From a diverse pool of qualified candidates, the most important consideration is judicial philosophy.
Here’s the issue of diversity and the Supreme Court in 60 seconds: