Hi,
Images from different scanners can look very differently (intensity, scaling, non linearities). Also acquisition parameters can change images and bias results.

This warning exists to make sure users understand that whatever they get out of the analysis could be completely driven by acquisition differences rather than disease/drug effects.

I don't know exactly what you are asking about FSL, but in freesurfer we conform to 1 mm isotropic. This does not correct or remove any of this acquisition bias, only it makes sure that all components work with the same resolution internally.

Depending on your study design (how many time point in each scanner, test retest on different scanners with short time distance etc) could be that you may not be able to draw any conclusions from your data. We once saw growing brains after a scanner software update. Changing hardware will be a large difference.
Sorry, Martin