The datasource for that flight track is ADS-B so it is going to be quite accurate (i.e. that’s where the aircraft actually was)
At worst you might have a lateral displacement if it’s not reporting GPS data for some reason, but (a) that should be minimal for a departure and (b) I don’t see it on that track (it’s uncommon)
They filed LOWGN7 but indeed the actual path taken diverges.
It’s not unusual at all for actual flight paths to diverge from the published/filed departure procedure. ATC is going to vector the aircraft in whatever way fits them best into the flow of traffic.
In terms of finding an area free of airport noise, I’d advise that outright distance from the airport would be a more important consideration than trying to suss out and avoid “common” departure/arrival corridors.
Here in the United States, very little effort is made by the regulatory agency (ie the FAA) to enforce noise abatement (climb/descent and lateral track) procedures that would be beneficial to the local populace living in close proximity to airports.
This is may be due, in large part, to the dual charter given to the FAA by the U.S. Congress back in 1958 for the agency to both regulate and promote air commerce.
Unlike Europe, Japan, Australia, along with numerous other countries where strict adherence to published noise abatement procedures are enforced with sanctions given for non-compliance, little is done in this country by the FAA to favor the general public over the airlines. (JMO)
For a captain who allows his aircraft to deviate from published arrival or departure tracks or noise abatement climb procedures at airports like Heathrow, Schiphol, Frankfurt, Haneda, etc…, almost assuredly his airline will be notified of the deviation and fined or possibly lose valuable landing/takeoff slots for continued non-compliance.