The shift in wavelength is primarily determined by temperature and current, and they work in opposite directions so sort of cancel each other out. And in any case, we're talking about well-characterized shifts on the order of a few nm over the operating range. The eye's cones are broadband, so you're not going to notice wavelength shifts, especially compared to the brightness variations over the same range.
This is a big deal for white LEDs because you have no control of the resulting color temperature (the phosphor emission and blue component wholly determine the output), but for an RGB structure, you have pixel-level control over each component.