Felines are the source of Toxoplasma infection. The felines are the natural host of this parasite which may cause serious infections in the susceptible host. This parasite is excreted through the feces of the cats and the cysts are found in plenty in the furs of the cats.
The furs do not cause diphtheria. Allergy (particularly respiratory allergies like asthma) to animal furs is very common.
You have to change the house in order to protect your child!