Strava is no different from posting up pictures of your cat on Facebook.
I use Strava every day, and it's fully private. Only I need to see my performance and routes. Only I need to work out my peaks and troughs and only I need to know exactly where I'm going and when I'm going there.
People yet again though, have in part, latched on to Strava as a way to showboat and parade like a peacock to their friends. I know of many people who routinely record runs and cycles going into hours, leading far away from their home area.
Combine it with some basic social engineering and interrogation of social profiles, I can find out where they live and know that every Sunday they bugger off for three hours on a bike.
Strava should really introduce an option to 'hide map' so you could still share your run data minus any geo data about it. Simply pace, elevation, time, etc. That way running clubs, etc, could still do their own things without being restricted, and people's location privacy is protected.