It is preferable not to but if you do make sure that the backerboard is tightly secured all the way to the subfloor under the hardwood. If the backerboard can move at all there is a chance that walking on the tile floor could crack the grout.
It is acceptable, not ideal, to install backerboard on top of hardwood flooring. The hardwood floor could be uneven, and could warp and expand with changes in temperature and humidity.
if you use backerboard on top of hardwood,it would be a good idea to lay some type of protective
material over the hardwood to keep from damaging the surface of the hardwood.
