You could change permissions to the Activity Feed and My Profile pages. Doing the above would generate an error if someone actually tried it. Better would be to replace those pages with ones that don't have the appropriate modules. Another approach would be to remove the links to those pages. Some combination of the above to keep out casual users, and to also keep out users who know how the default pages are constructed. You can also use the Profile Settings pages to make all profile fields visible only to administrators.
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