White protestant voters in 1996 were 53% Dole, 36% Clinton, 10% Perot.
White "Religious Right" voters in 1996 were 65% Dole, 26% Clinton, 8% Perot.
That's about as good as you're going to get, exit poll-wise.
You can also find state-by-state exit polls for the 1996 race here:
http://www.cnn.com/ALLPOLITICS/1996/elections/president/pres.return.html
White "Religious Right" voters in 1996, Clinton's share:Arkansas: 32%
Tennessee: 31%
Kentucky: 28%
Louisiana: 26%
North Carolina: 22%
Alabama: 18%
Texas: 17%
Mississippi: 16%
Virginia: 16%
South Carolina: 13%
Georgia: 11%
White Protestant voters in 1996, Clinton's share:Tennessee: 39%
North Carolina: 33%
Texas: 27%
Georgia: 24%
(These were the only Southern states that had this specific question in exit polling)