We have some members that are very active on Twitter/Facebook and that's flooding the Status Update with messages totally unrelated to the forum...
Especially Twitter is a problem.

I wish it was globally configurable if you want updates from Twitter/Facebook or not..

You can turn that off per member group.

Thanks. Do you mean Tools & Settings/System Setting/witter/Facebook connect?

But then also loose the ability to log in via Twitter/Facebook?

Members -> Manage User Groups -> Open the group -> Remove Status Import Ability

Aha, many thanks! Maybe it could be worth to mention Twitter/Facebook there so that the setting can be found via ACP search.
(it is mentioned in the description, but apparently that is not found by searching)

Can you remove it by user?

EDIT: I logged in as the user and shut off the connection in their profile settings.