As I understand it, the Church does not require anyone to believe the JEDP theory or any of its many "source criticism" variants or developments. Neither has the Church condemned these theories in general, as long as they are consistent with Church teaching about the nature of scripture.
Certainly, many people believe that many of the theories of source critics are mistaken. After all, many of them are contradictory and mutually exclusive. Some of them are downright goofy, as anyone knows who has ever picked up a wretched piece of nonsense called "The Book of J" that was a best seller several years ago. In addition, many believe that the usefulness of source criticism for understanding and applying scripture is limited. However, I think it would be hard to deny that the books of scripture in the form they have come down to us incorporate earlier documents and that the human authors of scripture sometimes used earlier documentary and sources, as well as oral tradition. Scripture refers to such sources. One example is at the beginning of 2 Maccabees (2 Macc. 2:23). Recognizing these facts does not undermine faith. One can certainly be orthodox and hold many theories of the source critics, including the JEDP theory.
On the other hand, no one is required to accept the myriad, and often contradictory, specific source theories of particular theologians or groups of theologians. It is certainly true that many of the proponents of these theories have taught things that are contrary to revealed truth and that some did not believe in God, in miracles, or in the divinity of Christ, for example. Moreover, many half educated people who learn a tiny bit about source criticism come away with the belief that that the critics have "debunked" the Bible. Therefore, Christians should not accept such theories uncritically, and should be wary of the error that is often taught along with them.
One of my main problems with the whole enterprise of source criticism is that it diverts one's attention from what God is saying to us to often fruitless speculations about exactly how He got it down in writing. There are few things sadder than some poor bloke who goes to a Bible study so he can know God's word better and who comes away spouting a lot of half understood form criticism and thinking that, as a result, he has made spiritual progress.
It is as if I sent you a letter telling you how to find a great treasure and, instead of using it to find the treasure, you sat there theorizing about where I got the stamp. Not that there's anything necessarily wrong with philately; it's just that there are more important things to do!
There are many excellent and reliable guides explaining how we can most correctly and profitably read, understand, and apply scripture, not least of which is in the Catechism. It's astonishing how many Catholic scripture study groups seem to lack any interest in studying them. I went to one such scripure study group for a few years that had been in operation for decades, that had never studied any of the relevant teaching documents, and that could not be convinced to do so (at least by me). It was saddening.