Even if you have “Activity Privacy Default” set to Private when you start an activity it pushes a notification to any followers that have favorited you. This is a serious breach of privacy.
Vote up the Feature Request (I agree, its a privacy issue and should be easily addressed).
The feature is one thing, but requires them to develop screens, an additional setting that has to be stored somewhere (their database) etc. This is a bug and a serious one. If people have their activities private by default they will expect that their activities are not notifying other people.
Someone could, for instance, follow someone they know who has their activities set to private but allows following and use this to determine when they are home. Not far off from the creepy stalker things Strava was worried about when it fixed a similar issue. And Strava fixed it in one day.
Even further, I’m pretty sure* the activity will still show up in your followers feed. They can’t click on the ride to see further data but can still see the basic info.
*I’m basing this on the fact I’ve clicked on activities in my feed and a message pops up saying something to the effect that the ride is set as private.