David Villa was born and raised in Tuilla, Spain.
He hasn't spoken about his personal religious views, but given that he's a Spaniard, it's highly likely that he, or at least his family, has something to do with the Catholic tradition.
There's a chance Villa is a bit intolerant of at least one religion. Villa was party to an international controversy when, during a game, Villa and opponent Mesut Ozil got into a brawl. Ozil said of the incident:
I did this because I was defending my religion because David Villa insulted Islam.
Unfortunately, that seems to be the extent of Villa's public commentary on religion.
Son of a miner's politics
Villa's politics are relatively minimal as well. He has sided with "labor" in the seemingly endless austerity strikes plaguing Spain. Villa's father was a miner and when coal miners marched in Madrid–fearing for their jobs–Villa expressed his support.
Other than that, no official political stances from the Villa camp that I can find. Let us know if anything changes.