We do know how a couple of the major denominations vote, and the Catholics sure vote for the pro-immigration side, while the major Protestant denomination is almost rabidly anti-liberal in their voting.
The Catholic vote is very different depending on ethnic group. A majority of white Catholics OPPOSED Obama, while a majority of Hispanic Catholics strongly supported Obama (as well as numerous Obama administration initiatives that the Catholic Church as a whole opposed, like the HHS mandate and gay marriage, etc.)
>> while the major Protestant denomination is almost rabidly anti-liberal in their voting. <<
The Methodist Church is an example of a "major Protestant denomination" in the United States. They are the second largest protestant denomination in the country, and the third largest Christian church overall. I doubt most people would describe the average Methodist as "rapidly anti-liberal" in their voting.
A couple other examples might fit your describtion, for example, I would say the Southern Baptist Convention is overall pretty rapidly anti-liberal in their voting. But again, if you were discuss the immigration issue specifically, if would break down as follows:
Most lay Southern Baptist members strongly oppose rewarding illegal aliens.
Most Southern Baptist clergy in leadership positions strongly SUPPORT rewarding illegal aliens.
Which again, is also true of EVERY major religious group in the United States. The lay people are against illegal immigration, their religious leaders are in favor of illegal aliens. If you know of any exceptions to this rule, please inform me.