Hey,
Thrust reduction (and acceleration) heights are airport specific, not operator or type specific. Each airport can prescribe a certain noise abatement procedure. You can read up on ICAO NADP A and B for the specifics.
Noise abatement procedures are not dependent on obstacles, performance, weather, etc. With all engines operating aircraft have no issues obtaining obstacle clearance in 99% of the airports. In case of an engine failure, special procedures are flown to assure obstacle clearance.