In this paper, we apply the frequency transfer function formalism to analyze the red, green and blue (RGB) phase-shifting fringe-projection profilometry technique. The phase-shifted patterns in RGB fringe projection are typically corrupted by crosstalk because the sensitivity curves of most projection-recording systems overlap. This crosstalk distortion needs to be compensated in order to obtain high quality measurements. We study phase-demodulation methods for null/mild, moderate, and severe levels of RGB crosstalk. For null/mild crosstalk distortion, we can estimate the searched phase-map using Bruning's 3-step phase-shifting algorithm (PSA). For moderate crosstalk, the recorded data is usually preprocessed before feeding it into the PSA; alternatively, in this paper we propose a computationally more efficient approach, which combines linear crosstalk compensation with the phase-demodulation algorithm. For severe RGB crosstalk, we expect non-sinusoidal fringes' profiles (distorting harmonics) and a significant uncertainty on the linear crosstalk calibration (which produces pseudo-detuning error). Analyzing these distorting phenomena, we conclude that squeezing interferometry is the most robust demodulation method for RGB fringe-projection techniques. Finally, we support our conclusions with numerical simulations and experimental results.