I tend to agree with the notion that people shouldn't be run out of projects (or organizations, or jobs) just because of their private beliefs, even when those beliefs offend me. It's too easy to imagine the mechanism that ran them out of town being turned around to run me out of town, should my beliefs fall out of fashion.
But as you note, there is a line where private beliefs stop being private and start being public. You put the line here:
> as long as he doesn't try to advertise that from within the project code, forums etc.
... but the developer in question was publishing the opinions in question on Twitter, which isn't exactly a private space. If you say something on Twitter, you are saying it in public. If you are a high-profile member of a project, the fact that the space doesn't have the project logo on it doesn't necessarily mean people aren't going to look at what you say and connect it back to the project. And it doesn't strike me as implausible that, if you're one of those developers and what you're saying is offensive to a group of people, those people are going to assume that the project you're the face of isn't a space where their contributions would be welcome. And that's going to hurt contribution to the project.
So I'm of two minds on this particular case, I guess. Which isn't very helpful, but does make it a question that I think could benefit from wider discussion. We as a culture have to hash out exactly where in these new online spaces we've created these new lines are appropriately drawn.