The eerie thing about every End-Of-The-World story in nearly every religion throughout history: they all mention the dead rising from the grave and walking upon the earth once more (granted, it isn't explicitly implied they're the flesh-eater variety of resurrected corpses, but, better safe than sorry).
Churches, especially the older stone cathedrals built by the Roman Catholic and Eastern Orthodox Churches at first seem like ideal places to fortify yourself when the dead rise. Stone and concrete walls, high forcing-you-to-look-toward-heaven windows, thick, heavy doors, well-supplied housing facilities for the parish and those seeking sanctuary, and often with one or more bell towers that could function as a prime sniping locations. For example, many Catholic churches, not even the larger cathedrals or chapels, in the United States were built in a time when they often had to defend against human-wave attacks, in this case usually being mobs of native-born Protestants rather than zombies, and were accordingly fortified.
However, churches rank low on the zombie survival meter, just as hospitals and police stations do. This is not because Satan's soldiers are trying to destroy the house of God: it's where the food is. As the rest of society falls around them, droves of people are likely to swarm to their nearest place of worship to pray for healing or miracles - only to be followed by the shambling undead, in slow and steady pursuit of their prey.
Even if a group does manage to make an adequate defense, there are going to be internal dangers. While few religious people are extremists, one is more likely to find extremist personalities amongst survivors making camp of a religious center. In every religion there are people who take their holy scripture as the word, and intolerant, even hostile or violent to anyone or anything that deviates from that belief even slightly. Extremist personalities are more likely to ignore logic or reasoning, which can prove a fatal flaw. As the situation begins to seem more hopeless, more and more survivors may to listen to the almost insane preaching's of these radicals. On top of all this, churches are one the most barren places imaginable when it comes to supplies. Stained glass windows, pews, organ pipes, and bibles can be found aplenty, but not so much when it comes to weapons, food, ammo, medicine, or fuel.
World War Z has several accounts of religious fundamentalists who have led themselves and the poor souls following them to tragedy, from child "mercy killings", to a cult who thought that the rapture was near and believed that the only way that they could ascend to heaven was to infect themselves and everyone else as soon as possible, with one group even making an attempt on the U.S. President's life. Also notable were accounts of a rampant religious sects spreading (and acting on) the absurd and disturbing belief that once one has sex with a virgin, one will be cleansed of the infection (echoing the same real-life false belief currently plaguing AIDS ridden African slums).
It should also be noted that there are often cemeteries in close proximity to churches, meaning that depending on the type of zombie outbreak these might actually be among the worst places to hide.
Being the epicenter of the outbreak. In some older churches the dead also used to be buried inside the church, though they would be covered by large heavy stones on top of their graves (from the church floor). But considering that some zombie outbreaks involve zombies crawling out of six feet of earth and a tough wooden coffin, that might not be a big deterrent for the living dead. Also note that there might be catacombs beneath larger and older churches. However many of the bodies buried in older churches will obviously be mostly devoid of flesh meaning they wouldn't be able to walk at all. Again, this is highly dependent on the type of zombie outbreak.