Should "Thrust Reduction" and "Acceleration" heights be the same for the Boeing 737 NG?
In absence of any other constraints, both thrust reduction and acceleration should be initiated at 1000 feet above aerodrome elevation:

Flap Retraction Schedule
During training flights, 1,000 feet AFE is normally used as the acceleration height
to initiate thrust reduction and flap retraction. For noise abatement considerations
during line operations, thrust reduction typically occurs at approximately 1,500
feet AFE and acceleration typically occurs between 1,500 and 3,000 feet AFE, or
as specified by individual airport noise abatement procedures.

(Boeing 737 NG FCTM 3.32 - Takeoff and Initial Climb)
Regarding your thought of

I always thought one does not reduce thrust before cleaning up but reading some posts I am in doubt now.

It is actually quite normal to reduce thrust before accelerating and retracting flaps. During NADP 1 (Noise Abatement Departure Procedure), which is most common around the world, thrust is reduced first (typically between 800 and 1500 feet) and acceleration is initiated later (typically at 3000 feet). For NADP 2 both occur at the same time. I don't know any procedure where thrust reduction occurs after acceleration.

Both heights can be set independently on the TAKEOFF REF page 2:


Thrust Reduction (THR REDUCTION)
Altitude above origin airport elevation at which the autothrottle reduces from
takeoff N1 to climb N1.
The default value is determined by the airline and is stored in the model/engine
database. The default is displayed in small font.
Manual entries allowed on the ground. Entries must be between 800 to 9,999 feet
and are displayed in large font.
Acceleration Height (ACCEL HT)
Displays acceleration hight for flap retraction.
Default value is from the airline.
Entry is optional. Value is a height from 400 to 9999 feet.

(Boeing 737 NG FCOMv2 11.40 - Flight Management, Navigation - FMC Preflight)