There's no realtime tracking, the activities are uploaded to Strava after finishing them. It can become a potential security issue if you upload activities from far away from home.
I find the bigger security issue is recording close to home, so people can theoretically see where you live and know what sort of expensive sports equipment you might have.
https://road.cc/content/news/248798-cyclist-who-had-five-bik...
And if someone shows off their expensive bikes on social media (and that's what Strava is, among other functions)... well, it makes it known to others that they own expensive bikes. Social media has been around for long enough that its users should be aware that this kind of behaviour may impose certain risks.