[my name] you can always speak to me and I don't know of anyone who hates you you're such a lovely person. If someone says this to you, would you think that they were your friend/cared about you?
Yes, that sounds really supportive to me and as though they care.
I'd be careful of pulling away from people because their behaviour is deemed as 'fake' by some. Before I knew I was an autistic individual there were many times in my life where I followed a social script as I wanted to say the right thing. Although it wasn't natural and may come across as fake good intentions were there.