Religiously, Jews are staunchly Democratic, 55 percent to 18 percent, and likewise atheists favor Democrats, 31 percent to 15 percent. Unfortunately for Democrats, white Catholics have been trending Republican in recent decades, and the survey I'm using to write this put white Catholics at 32 percent Democratic and 31 percent Republican. White Protestants are overwhelmingly Republican, 40 percent to 26 percent. Of those, evangelical Protestants are even more Republican compared with mainline Protestant denominations. Additionally, the more orthodox views and the greater frequency of church attendance white Christians have, the more likely they are to be Republican.
This doesn't answer the question of what the composition of the Republican party is, but what percentage of these racial and religious groups identify with each party. Courtesy of Gallup, subscription needed, article by Lydia Saad dating from July of 2000.
In terms of gender, men outnumber women in the Republican Party by a six-point margin, 53% to 47%. By contrast, women outnumber men among Democrats by a 14-point margin, 57% to 43%. And if the Republican convention hall looks to be noticeably lacking in minorities next week, it could be because the party at large is 93% white, with only 3% of Republicans reporting to be black and 4% reporting to be other racial minorities such as Asian or American Indian. While a majority of Democrats are also white, the proportion is much lower, at 75%, while 19% are black and 6% are other minorities.
A graph shows religion: Republican Protestant, Roman Catholic, Orthodox(Christianity), Mormon and other Christian categories are 44%, 24%, 1%, 3% and 6%. 78% total Christian. Democrat percentages for the same groups are 34%, 25%, 1%, 1% and 6%. 67% total. (2%+/- margin of error)
I saw several articles commenting on Dean's statement that mentioned a CNN/Gallup/USA Today poll that said 82% of Republicans and 57% of Democrats are white and Christian, but couldn't find the poll itself, so I don't know if that degree of overlap is accurate.
Census Bureau DP-1 Profile of General Demographic Characteristics: 2000 says 75.1% of Americans are white.
Gallup's numbers on Christians in 2000 is 52% Protestant, 25% Catholic, 1% Orthodox, 2% Mormon, 5% Christian non-specific. As of May 5th, 2005, the Protestant percentage declined to 48% and non-specific Christian rose to 7%.
So whatever anyone wants to make of it, there are the numbers.