But what about Ha and R filters for example?
LinearFit works under the assumption that the differences between pixels with the same coordinates in both images can be reasonably well described by a straight line. This is the only condition. When this condition doesn't hold, the achieved result is not valid, not because LinearFit fails, but because the problem is a nonlinear one.
In the case of Ha and R I think there should be no major problems, but it depends on the images. If you upload them we can make some tests.
They could both be different exposures and binning
Exposure differences shouldn't pose any problem, since the sensor's response is linear. If the images have different sizes, this will already be fixed in the previous---and necessary---image registration step.
I tried using the Ha as reference and applying it to the R, then tried the opposite with R as ref and applying to Ha. The results were different.
This should not happen. Could you upload the images so we can get them a try?