Are you disputing whether they should be allowed according to our current laws, or whether they actually exist? There are plenty of women-only or men-only or black-only or Jewish-only or Chinese-only or ... etc. private clubs/organizations. For example Augusta National Golf Club only recently admitted women, and solely due to public pressure / protest; not due to any legal requirement as far as I know.

Whether they should. I'm absolutely sure there exist organizations that break the law exist (sidestepping the issue of whether or not this does break the law).