Should air vents at crawl space be open on a house during summer?

Yes, especially if you live in an area where the humidity is higher. The vents allow moisture in the air to escape from under your house. Moisture trapped under your house can cause mold and floor rot. The vents should always be open a little. This is to ensure you don't get a sick home and so the air circulates through the house. That's if these are hvac vents. If the vents go to the outside, they should always be closed.