Note also: Often the club contact person is NOT necessarily the match contact person. (Many times, the people who run discipline-specific matches are volunteers who love that sport, and so they aren't necessarily club officials or anything.) I don't know who exactly you tried to email, so if you emailed the match director, I'm sorry to hear they couldn't respond to a simple email in a timely fashion. If the person you tried to email wasn't the the match director, though, while that may say something about the club/range, that doesn't necessarily say anything about the match and match staff.
As many people have said: In most places, you do NOT have to be a member of the club/range to shoot USPSA matches there. (That's actually part of the USPSA affiliation agreement, that USPSA members must be allowed to shoot unless certain circumstances occur.)
When all else fails, call the match director or match contact person directly, and go through the anguish of having to speak directly to someone (bleck!). Generally, you'll find they are happy to give info and get you into competition shooting.