I attend the Golf Course Superintendents Association of America conference every year as a vendor. That profession has one of the highest rate of cancer of any profession due to the herbicides, insecticides, pesticides, and fertilizers they are exposed to every day. It's so prevalent, that a significant amount of the training they go through at these conferences includes dealing with cancer insurance claims.
It's not a stretch to assume that some of these airborne chemicals can also impact the residents who live next to a golf course. The guys spraying this stuff are wearing gloves, respirators, and long sleeves. That stuff then drifts into your yard where you have none of those protections. If I had a home on the course, I would NEVER leave my windows open, and I would only enjoy the outdoors well after the chemicals had been applied and the grass had been mowed.
Europe bans most pesticides and insecticides because of these reasons. There are alternatives that can keep the course in top shape and reduce the known health risks. But they are expensive and would require regulations to force compliance.
Here is one of thousands of articles on the subject -
Pesticide Dangers at Golf Courses Much Higher in the U.S. than Europe, Study Finds - Beyond Pesticides Daily News Blog