Can you safely have a pet gecko with a child with cancer in the house?

It depends.: Many exotic animals, like geckos may have certain pathogens that will build up on them if they aren't meticulously cared for. Moreover, if a child has cancer, or is undergoing therapy for it, the child is most likely immunocompromised, and vulnerable to infection. It may still be possible to have this kind of a pet, but preparation and at least discussion with your doctor is needed.

No: I've never been impressed with the fascade of safety that staff and parents wear masks, when the child harbors pathogens, and the hospital environment is contaminated with very virulent bacteria, and the human mouth is more dangerous than a dogs...I cannot imagine that a gecko carries something critical. The charade of masks and gloves provides an illusion.