Adele, whose real name is Adele Laurie Blue Adkins, was born in London, England and grew up in various places throughout southern England before completing her formative years back in London.
Adele is relatively new to fame and as such, hasn't been subjected to the requisite scrutiny over a celebrity's religious views. Even the numerous question and answer sites seem to be unwilling to speculate about Adele's religion. But her time will surely come.
However, it is reasonable to assume that Adele, being a white Englishwoman, probably has Anglican/Episcopalian roots and, if forced to, would probably identify as Christian.
Conservative–for personal reasons
Adele is a bit more interesting politically. In fact, she might be considered somewhat conservative. She was pretty fired-up over her tax bill and the British government's use of her money, saying:
I'm mortified to have to pay 50 percent! [While] I use the NHS (National Health Service), I can't use public transport any more. Trains are always late, most state schools are shit, and I've gotta give you, like, four million quid – are you having a laugh? When I got my tax bill in from [the album] 19, I was ready to go and buy a gun and randomly open fire.
There you have it, a British celebrity standing up against the European welfare state. It's rare, and her publicist probably wasn't too happy, but the girl speaks her mind.