I recall it was pretty easy for people to just friend each other on MySpace. And to a lesser extent Facebook, but most people treat FB like a digital rolodex of IRL personal contacts and were more hesitant to just add any randoms to their friend list.
The only way you can get to be part of a community that feels intimate is where it is niche and hasn't become part of the internet mainstream. Forums centered around highly popular web figures are often very big.
But you can still find good forums. Forums that are built around very specific interests are more intimate and it's more conducive to comfortably talking to strangers and develop online friendships.
Also, this is just from my very casual observation, but forums built around interests that are not typically associated with more mainstream geek culture or tech culture, that are not privy to highly polarizing social views seem to have the air and attitude of the older internet.
Some example topics for such communities may be bird watching, crocheting, trade jobs like plumbing or modding/tuning for very specific older cars. These have a different demographic (usually skew older) and attitude towards conversation with strangers than the demographics that attract more people on topics such as gaming computers, comic books, anime, etc.