The Tacoma Narrows was nicknamed "Galloping Girdy" because the winds could cause it to sway.
Then, one day, the wind came howling at just right angle at just the right sustained speed and it caused a longetudinal resonance in the bridge that became out of phase between the two sides. The hours of wind caused violent twisting that eventually tore it apart.
As to the Golden Gate, I'm sure that the few people near the bridge could find it annoying, but people stating that they can hear the bridge miles away is total crap.
Given that the bridge runs almost exactly north to south, no one toward either end will hear much of this since the bridge will act as giant line source. You might hear it if you lived at the eastern section of the Presidio and it may be a very gentle murmur in the Marina District, but that's about it. There are not a lot of people living close to the bridge. Check out a map.
I live a half mile from commuter train tracks. When Amtrak goes blasting by, it's not very loud.
Honestly, I can't see how a gentle drone note caused be the wind is really going to be that bad.
Like the Big Dig in Boston or elevated trains in Chicago, after a while you won't notice it at all.