I'm going to give you a bunch of different options. There is a slim chance that you'll actually like any/all of it, because it doesn't sound a whole lot like Disturbed. But it does have fast drum and guitar, and nothing that I listen to regularly is anti-Christian.
The vocalist from 3 Inches of Blood has a 80s-metal voice to him.
I can't believe I'm recommending it, but Shadows Fall has a lot of good metal with a non-screaming vocalist. I just can't stand his voice.
Also, Killswitch Engage's newest album has the least amount of screaming, and you might like trying out their style as well.
I second Chimaira as a recommendation as well, although again, the newer the album the less screaming there will be.
Also check out Every Time I Die for a different metal sound, more reminiscent of Southern Rock but with metal/hardcore roots. "The Big Dirty" is their latest release and has the most vocal variation. Older albums will be almost purely screaming. "Gutter Phenomenon" has a different vocal sound to it. Check out the song "The New Black." You will like the cowbell.
And for more southern rock/metal and less hardcore roots, Maylene and the Sons of Disaster are also a good option.
Swedish metal often has a lot of scratchy vocals, but In Flames' vocalist would probably be the most tolerable for you, and their newer album "Come Clarity" again would be the best one to check out for cleanest vocals.
For a more interesting take at metal, in this case it could probably be considered mathcore, Protest the Hero is a great canadian band with clean vocals and really really fast pace changes and instrumentation.
Pure Metalcore, which may not be what you are looking for, has more options that I could recommend to you. All That Remains' album "The Fall of Ideals" might be a good start.