According to the International Agency for Research on Cancer (IARC), talc-based powder when used on the genitals and buttocks is ‘possibly carcinogenic to humans.’ Talc that contains asbestos is definitely carcinogenic.
Many experts would say modern talcum powder is safe for use around children. But it is understandable if the concerns about cancer would have you not want to use them around yours. There usually are good alternative products available that do not contain talcum powder. For example, cornstarch-based products often can be a solid substitute for talcum powder.
Even without the cancer risk, the inhalation of baby powder containing talc or cornstarch can cause respiratory issues in children. You should avoid putting talcum powder directly on the genitals. Do not get baby powder in a child’s eyes, and keep it away from you and your child’s face.