Talcum powder today is generally recognized as safe and not containing asbestos. It was mostly decades ago that some talcum powder was found to contain traces of asbestos, which can cause cancer in humans and animals. Many experts would say that it is safe to use talcum powder around your pets. Talcum powder can also be used as a dry shampoo on dogs. But if you have any concern, you can always buy dry dog shampoos at a pet store that do not contain talcum powder.
Also, if you are worried about using talcum powder-based products around your pet, it is recommended to review the product label of such products. There usually are talcum powder-free alternatives on the market that you can use instead.