In most cases, the answer to this is yes. There are few reports of major side effects reported from using the best of anti-chaffing creams--and those that are reported are minor and short-lived. However, if you're dealing with chronic illnesses or conditions that affect your skin (psoriasis, eczema, or skin cancer) you need to talk to your health care provider before you begin using any of these products!
This is to help ensure there are no risks for interactions or side effects.