Thankfully the answer is pretty easy, though it can take some time: a routine maintenance called stripping. The idea is to strip the detergent residue out of the fabric. Successfully done, it will improve absorbency, reduce odors, and help your baby stay rash-free.
If you google "stripping cloth diapers" you'll find dozens of ways to do it. Some are easy, some are unbelievably complicated. Some methods void warranties. Here are the three methods I recommend most often. These methods are accepted by most of the major cloth diaper brands.
1. Hot Water - try this one first...it's easiest! Simply wash diapers and inserts as usual, then rewash in hot water 2-3 times with no detergent. During the agitation cycle (preferably hot water agitation), look inside your washer. If there are any soap bubbles at all, run another hot wash. Repeat until water is absolutely clear.
2. Oxyclean - either the Regular or the Baby version will work. Wash diapers as usual first, then rewash in hot water with the amount of Oxyclean recommended on the label (usually 1 scoop). Rinse 2-3 times until water runs very clear.
3. Dawn dishsoap - this one is overall the most effective, but takes the longest. Use original blue Dawn. Wash diapers first, the rewash in hot water with 2 tablespoons Dawn. Then rinse and rinse until water is clear. This can take a while to wash out all the Dawn bubbles. It's extra bubbly since it's not made for washing clothes, but it works very well to strip out detergent residue. If you have hot water rinse, that will be faster. If you can't get them bubble-free in 2-3 washes, then I recommend going ahead and using them, but running 2-3 washes when you wash them again. That way it breaks up the number of washes needed to get the water to run clear and you can use them in between.
Other popular methods include using RLR (little balls of detergent found in the detergent aisle) or soaking with Rockin' Green. I haven't personally tried these methods, but I've heard great things about them. These methods are also not mentioned much by the manufacturers, but I don't think they would void any warranties.
Just one last note: if you use dryer sheets or fabric softener with your regular laundry, it can transfer residue from the machine to your diapers. Use the same methods to strip out fabric softener residue. Then I recommend using a scoop of Oxyclean once every week or two to prevent buildup from occurring again.