The charcoal inserts are safe. The material is mostly polyester with some bamboo charcoal woven therein to aid with the wicking etc. Polyester allergies are very rare indeed (and usually reactions are to such things as stuffed animals ... the dust etc which migrate to the "fur" of the stuffies).
The rare times we hear back from parents about any rashing and our charcoal inserts, the culprit is generally an infrequent change routine (thus, ammonia and eventually bacteria build-up). The charcoal has more a "stay dry" feel to it thus parents and caregivers might not realize the diaper insert is full right away.
Give each a try. The products are safe for use. Remember the key is a frequent change and laundry routine. Cloth is great stuff, but it fills up faster than disposables, sad to say but true.