I don't think there is a way to change the access to the /activity page (and actually to any question list). In fact, taking a look at your site, it is public. So it makes sense that Google indexes.
What you seem to have disabled is the Viewing question pages setting for anonymous users. Bear in mind there is also this setting Allow search engines to view question pages. The setting is a bit trickier than what the name says but basically it will allow "non-common" user agents to access questions (which, in fact, is a way of making question accessible by the public, taking the additional effort of changing the user agent).
