Though it is not explicitly dangerous to your health, we do not recommend that you use the yoni egg during your menstrual time. Better to give your uterus space to release the monthly blood without adding any extra stimulus.
That being said, wearing yoni egg during the moon time is something you need to decide for yourself – trust your intuition. If you feel comfortable using it during your moon time, go for it! Just make sure to clean your egg thoroughly before and after each use, as you are more susceptible to infection during this time of the month. Do not wear it for longer than you would a tampon to allow blood to leave the body.