I use and sell cloth diapers and my answer is - try it. It may work for you. Depending on your water, you may not have any problems at all. I use Tide because it seems to be the only thing that doesn't cause smell/build-up on mine. Also, if you use natural fibers (i.e. cotton prefolds) you have a lot more levity in the kind of detergent you use. The synthetics, which is more of what I have, are pickier about the detergent. Always do an extra rinse to get more of the detergent residue off, and you may be pleasantly surprised.
If you aren't comfortable with trying the Free and Clear, why not just use it on your regular laundry and stick with what you know of diapers? Then you have cheap detergent to use up without messing with your diaper laundry (and the possibility of having to strip them). For what it's worth, I do a medium load cold rinse - to get the poop off - the longest, hottest, largest wash with the regular rinse, then an extra cold rinse on medium size load.
Oh, and like some others say, I use bleach occasionally too. Especially after my son got to toddler age - that stink seemed to hang around longer. And I know what people say about it breaking down fibers, but sometimes they just need it! I only use about 1/4 cup and then make sure they get rinsed well b/c one of my son's has very sensitive skin. My diapers are now working on kid number 2, so I couldn't have screwed them up too badly!