I don't think the word "inauthentic" quite captures why people react negatively to this sort of communication.
At least part of it comes from the fact that this particular style of "kindness-is-cool-coded" (for lack of a better word) communication happens to be the preferred style of insanely passive-aggressive people who take it upon themselves to brutally sabotage anyone who they deem unacceptable. It can also feel like you're being lead on by someone who actively dislikes you but is too polite to say it. Or you just start second-guessing every single thing they say and do.
But honestly, there's a pretty sizable minority of people who are repelled by this type of person and if you're naturally bad at reading the room you're probably better off making friends with other people that say and do dumb things.
I know I went through a "How to Win Friends and Influence People" phase when younger and basically ended up just putting off a whole of people.
Likely stems from a hundred and fifty odd years of the "always British" types swanning it over the "this is where we live and we love it" crowd.
Aside from being about forming sincere relationships, it handles influence with essentially this advice: Stop trying to force people to care about what you want. Understand what they want, treat them with respect, and align your request with their self-interest and self-image. If you come off as false doing those things, it’s because you didn’t actually do them, you pantomimed them.
“You’re such a generous person. I know you love being there for friends. Could you help me move Saturday?”
It's an example that of course sounds ridiculous to anybody that reads it, but it's essentially what the book teaches. Gather information not even about the person but how the person feels about themselves and then use that as a tool to make them feel good when you're talking to them.
I suppose it's also not helped that many of the people I've met who use this and admire this book have psychopathic traits. They're very good at faking caring but actually can't. It's a cold calculation to them and admittedly it's very effective at getting them ahead.
Manipulation seeks to get someone to do what you want against their interests.
Persuasion seeks to align their interests with your interests in a mutually beneficial manner. The act of speaking to their interests by definition takes their well being into consideration.
I don’t know how you could read that book in a modern frame and get syrupy insincerity out of it in good faith, but it is true that many people read this type of book looking for shortcuts and hacks, so they are not looking for the good faith reading. If you read the rest of NH’s work, you will find that his philosophy is firmly based on genuine good faith and delivering disproportionally high value to the people you interact with. (As well as some very 19th century metaphysics you can safely ignore)
But yes, many people read that book, ape the ideas, and act like asshats. It’s hardly a failing of the book.