Technically, it's classifed a re-engined Stage 3 aircraft.
Trump's complaint is not about the existing noise issues; it's about creating a new runway south of the existing main runway that would put flight paths directly over Mar-a-Lago - significantly altering the airport's noise footprint. In this case, he has a legitimate gripe.
You can complain about people that move into the noise footprint of an airport (me) and start complaining (I don't), but in this case the issue is much larger than just noise.
The runway expansion project was kept secret by the airport staff and was sprung on the local taxpayers with not so much as a courtesy memo to the Palm Beach County Committee on Airport Noise or local municipalities. The EIS (Environmental Impact Study) was started based on an FAA report that cited the need for additional concrete based on "economic factors" and not on an analysis of the actual traffic needs. (Burbank is the only other airport that the FAA used economic projections as their primary determinant instead of traffic projections based on real numbers.) The entire project is supposed to prevent taxi delays from increasing to 20 minutes in the next 10-20 years (I'll have to look up the actual timeframe.) Seriously, that's how they are justifying spending a half-billion dollars of the taxpayers' money.
The FAA/ATC has said that more concrete won't do anything for the bottleneck out of south Florida and won't significantly speed up departures, but nobody is listening. On top of that, the runways will be less than 800 feet apart - which requires traffic spacing to be the same as a single runway operation when there is weather. Want more? They want to shorten the 14/32 to 4000 feet - rendering it useless to most of us when the winds don't favor 10L/28R. Does anyone want to guess what happens when a tropical storm or hurricane moves through the area? The airport closes hours earlier and stays closed much longer after the storm passes because the crosswind runway is too short.
The entire project is ill-conceived, but is all part of the empire building that the Director of Airports has been known for.