Are there any fabric softeners I can use for my baby's clothes?

No. Do not use fabric softner for infants, children or teens with eczema. The fragrance and other chemicals will almost always make their eczema worse.
Yes. While I don't recommend the routine use of fabric softener, some infants tolerate any fabric softener without problems. For most infants, however, it is best to avoid fabric softener altogether and give laundry an extra rinse before placing in the dryer. Softeners contain fragrance and other chemicals that can be irritating to sensitive, young skin.