When I cd'ed my 2 younger girls, we had to wash at the laundry mat. I never had a problem with products others had used before me at all. I never had a build up issue ever & still have the same WAHM fitteds I had made 10 years ago. I think it should be fine. :)
We share machines with my husband's parents. I use Charlie's Soap so I attempt to do a load of non-diapers with Charlie's before I wash diapers. I believe this is working to keep residue off of the diapers because the detergent residue has already clung to the first load.