I think that it would help if you define what you mean by socially conservative. If it means being anti-gay and pro-religion, Memphis is a strong candidate. If it means taking responsibility for your life and your family, not at all.
I was thinking of the former, though I wouldn't limit it to anti-gay and pro-religion.
Wouldn't the latter be more economic conservatism?
I see what you're saying, but I just can't see a city with teenage pregnancy, drug abuse, high crime, etc, as much as Memphis as being socially conservative. Ditto for the acceptance and often expectation of corruption in local officials.