I don't think Hillary Clinton will be hurt in the south from representing a northern state with the exception of Arkansas which she abandoned as too good for.
Arkansas was her best state during the primaries, so I highly doubt that the voters there think she left them because she was "too good for them." They just named the Little Rock National Airport in honor of her and Bill. Some even argue that her not being the nominee was the reason why Arkansas swung so heavily Republican in 2008.
As per religion, here is what I was able to find per The Association of Religion Data Archives (ARDA):
ARIZONA• 62.77% Unclaimed/Not Religious
• 14.55% Catholic
• 11.93% Evangelical Protestant
• 6.18% Mormon
• 2.69% Mainline Protestant
• 0.19% Black Protestant
GEORGIA• 49.17% Unclaimed/Not Religious
• 29.45% Evangelical Protestant
• 8.83% Mainline Protestant
• 6.16% Catholic
• 3.94% Black Protestant
• 0.81% Mormon
Also, in terms of veterans, Arizona has 11.02% whereas Georgia's is 9.43% statewide among the total adult (18+) civilian population.