Some of the best people I've known in life have been believers
Likewise - and from a similar range of backgrounds. However, to the extent that their beliefs contain things I find abhorrent, I see their 'native' generosity as being constrained by religion, not the result of it. Certainly many of those I know who started as believers and came to reject the beliefs they were raised on did so from the dissonance between principles and expression, internal inconsistencies or an internal growth that left the original belief system behind.
More, some of the most dangerous and damaging people I have met have been fervent believers. Some have used their belief system to justify behaviour that is essentially self-serving. Others, from genuine belief that what they were doing was 'right', have caused more harm than the first group.
If you should encounter a really horrible person online, say on a forum or Twitter or something, chances are very good that they're atheists
There are certainly a lot of nasty, self-important people who are atheists. Just as there are plenty who are Christian, Muslim, Jew, Hindu ... I suspect a degree of confirmation bias in your assertion.
but because being horrible almost requires non-belief
As T.S. Eliot observed “Most of the evil in this world is done by people with good intentions.” Belief can be, and often is, used to justify action that would otherwise be clearly horrible.
they tend to stick out because they tend to make a spectacle of themselves
As do your online atheists, above. How can you tell an atheist who doesn't loudly announce it at every opportunity?
but belief seems to have the properties of a good ingredient.
Unquestioning belief can be blind. Unchallenged belief is limiting. Unexamined belief can be stagnating. In as much as it's easier to co-operate with people with whom you share a common belief, belief builds communities - but it's a short-cut to really understanding and acceptance of an individual. As you say, all too often it becomes tribalism by another name. Just because some people can be amazing and also believe says little about the worth of belief.
It's almost as if the part that makes you better is the process, more than the specifics of any faith tradition.
With this I am in total agreement.