I'd like to know if there is any problem in using resistors of some kOhms as RF and RG for ADA4937 fully differential amplifier: I need a 2kOhms input impedance.
In terms of functionality, you shouldn't have any problems if you use resistors in the kohm range for Rf and Rg. The only issue I would see is that using resistors in that range would add a lot of noise to your system. You usually wouldn't want to add components around the system that negates the performance of your amp. The ADA4937 is a low noise amplifier, with about 2.2nV/rtHz input voltage noise. A 1kohm resistor alone at room temperature has a noise voltage of 4nV/rtHz at room temp. If say for example your amplifier output goes to an ADC, the additional noise could degrade the SNR and consequently, the ENOB of your system.
If you want to have an estimate of the amplifier performance given your setup, you could use Diff-Amp Calculator. It's downloadable at this link. It gives approximates of noise, power and bandwidth parameters that might be helpful for you.
I hope this helps!