IMO it's completely fine. I would be more annoyed/worried about calcium deposits on the paint from when the water dries.
.........And I know you already said it, but change the sprinkler heads to the type that deflect from the driveway. They exist and usually aren't expensive. Your car is more important than the grass![]()
I only wash the cars with irrigation (river) water to avoid any hardness the city water contains. After the first wash of the car there was some large drops accumulated on the flat part of the bumper under the trunk after I dried it, and then moved it into the garage. What was previously water stuck in the trunk gasket and heading downhill, is now water draining out. Anyhoo, the droplets dried and left circles of whatever chemicals are in the water.
No more. The irrigation water might be full of tiny seeds, but no more spots.