Manure and organic waste excrete hydrogen sulfide while they are being digested. The rotten egg smell you speak of is the hydrogen sulfide and it is toxic. And one of the major symptoms of H2S poisoning is migraines, coughing, shortness of breath.

So your neighbors were completely inline with feeling the way the do.

BTW, I went to school next to a mushroom farm. A big warehouse with giant mounds of manure. And yeah we felt all of that too during the warmest times of the school year. The school administrator and most parents tried to convince the students it was all in their head.