Triple H, whose real name is Paul Levesque, was born and raised in Nashua, New Hampshire.
Some people seem to think Triple H is Catholic, but I couldn't find any information from the man himself confirming this. On his MySpace page, his religion is listed as "Christian – other," which neither confirms nor denies the rumors.
And so it would appear that Triple H is some sort of Christian, but he's either not very religious or he likes to keep it private.
Triple H appears to be a Republican, or at least a supportive son-in-law. He is married to Stephanie McMahon Levesque, the daughter of Linda McMahon, former CEO of World Wrestling Entertainment and Republican politician. During McMahon's unsuccessful 2010 run for Senate in Connecticut, Triple H campaigned for his mother-in-law.
I couldn't find any evidence that Triple H actively campaigned for McMahon during her 2012 bid for the Connecticut Senate seat, but he did attend that state's Republican convention in 2012 with a few of his in-laws.
I couldn't find anything else from Triple H about his views on specific issues, but we can suppose until we hear otherwise that they're in line with the Republican platform.