As someone that had the unique experience of gaining over 7.5cm or 3 inches in height after becoming an adult thanks to a surgery that "fixed" a spinal deformity, I have to say that I got treated noticeably better by strangers after getting taller, women and men. It's like I automatically got treated with more respect. And it was an immediate thing too, while I was still recovering from surgery, underweight and walking like I had a board stapled to my back. Once I recovered further and gained weight and mobility, I got treated even better. And it wasn't as if I was short before either, I went from around 177cm/178cm to 185cm barefoot, or 5'10 to 6'1 in imperial measurements.

So yes, at least in my experience, society is as shallow as you think, in fact it ended up being more shallow than I ever thought. Which is why I've found the whole thing surprising. I never expected to just get treated better because I got taller, that was never one of my issues or concerns. I wasn't completely naive, I knew that I would get treated better by society if I didn't have a visible spinal deformity thanks to all the bullying and unwanted comments I recieved on it, but I never expected height to play such a large role. It really changed my view on this, I always thought shorter people were exaggerating about stuff like this. Though the worst I've ever been treated in public is when I had to use mobility aids and my spinal deformity was visible no matter how baggy my clothes were. I got so many stares that could give you nightmares.

As for dating, I've always struggled with that, I'm bisexual and don't really gel well with the heterosexual dating dynamic, traditional gender roles, etc. I never really dated that much before the surgery. I got a lot of unwanted comments about my posture from girls and women though. I do find that I get more attention now, but height is only a part of that. Not having a visible spinal deformity and being a healthy weight also plays a big role. But yes, height does play a part, and I'd be lying if I said it didn't. But for me the big difference hasn't been in dating or attraction, but how people treat you in general.

Overall people are shallow, it's not great but it is what it is and I can't see that changing.