Use the Hardiebacker. Put a vapor barrier behind it, lapping the bottom edge over the tiling flange of the tub. The sell shims at some lumberyards that make it fairly easy...tack them up, put up the vapor barrier, then the Hardie.
Often, the tile extends beyond the outside of the tub itself. Since that area is typically dry, you can end the cbu there, and put the outer row of tile on the drywall. Use the mesh tape.
If the studs are not plumb, sometimes it is easier to add in sisters to get the whole wall plumb rather than shimming th eold ones out. Keep in mind that with the thinset under the tiles, you may not need as much of a shim as you think. That outer edge only needs a small amount, and the thinset over the Hardy should be plenty. If it was on a floor, that'd be a different thing, but you're not walking on the walls. You don't want that last row to bow out, though.