My child has gastroenteritis, my breastfeeding increases his diarrhea. Should I stop breastfeeding?

No. Breastfeeding is the best choice for your baby. However, if it persists, you should speak to the pediatrician to see if any further work up may be necessary to rule out any metabolic disorders.
No. He probably had a temporary lactose intolerance and your breast milk has lactose. If you continue to feed him, his small intestine will be stimulated to grow back faster and handle the lactose in your breast.