Feel free to refute this, but here’s an article I found that suggests there’s little evidence that Head and Shoulders is bad for your hair - at least the ones that aren’t Clinical Strength.
Minor anecdote: I used to have severe dandruff, then I started using Aveeno’s Apple Cider Vinegar products and that helped a LOT, but now I use the ACV H&S and I haven’t had any real complaints since the switch.