I agree with putting a membrane over the hardibacker; Red Guard works quite well - 2 coats. The reason for the felt is for future protection in case of water penetration to the hardibacker. Just a tiny bit of settling and you could end up with a crack along a corner.
So, OP: gut it down to the 2x4's, install new tub, plumbing, etc.
Then: felt paper (I've seen some videos on youtube where contractors use a thicker plastic; and they only go up as high as the wall is going to get wet.) I've also seen at least one contractor on youtube using the sticky flashing stuff that you use to seal around exterior windows when doing house wrap - that could be used around the lip of the tub, hidden by the hardibacker and tile.
Then, hardibacker. Seams of hardibacker get taped with an alkali resistant tape, and thinset. (Like doing drywall seams, except drywall tape isn't resistant to the alkali in the thinset.)
Then Red Guard, 2 coats.
Then tile.
Then grout.
Learn how and where to start your tile - first row does not go against tub - that's the last row you do. Start 1 row up, and attach a ledger board to keep your starter row perfectly level. It's really not hard to do if you watch a bunch of youtube videos on the best techniques, and pay VERY close attention to details. Plan out all of the tiling, measure multiple times, to make sure you don't run into problems where you start and where you finish. You don't want a row to need to be 1/4" wide or something.
One of my friends just hired the same contractor I tried to politely tell her in the past was cutting way too many corners. She just had a custom shower put in by that contractor. The entire construction was regular 2x4's and drywall, with the exception of a seat in the shower. The top of the seat was hardibacker - the front of the seat was drywall !!! Then, he tiled over the drywall. The floor prep: drill hole in existing floor, install drain lines and floor drain fitting, tile over existing floor. No slope to the floor at all. I sent link after link to her, showing how to do the job right, and suggested she research and stop him before he tiled. But, his last job he did, right before they moved out of their old house, looked so nice. And, the finished product on this one *looks* nice. It'll be lucky to last 3 years.