Sharing activities with just one person or "closed connection"

You could add only closed friends as Connections, and sharing data with anyone else through groups. In this way only Connections (closed friends) will see activities you share with Connections, and all other friends in Groups will se only activities you share with Groups. 

This tips seems to not work since I cannot choose the privacy just for groups but "connections & groups" only.

I mean, it is a such security improvements that I cannot understand why Garmin has not implemented it yet.

As I wrote, you can share an activity just with Connections, so only your close friends will see them (as long as you directly connect only with close friends).

And if you want to share the activity with a wider number of people (including non-Connections from your Groups), the you can choose the privacy level "Connections & Groups". 

In other words, it is as simple as not connecting directly with people you do not want to share your activities with. Keep those people that you want to share some activities only occasionally, in Groups, without connecting to them directly.

Thanks, understood.

However the main problem, that I have to force people to join a group, remains.

Simply send them an invitation from the group. If they do not join, then they apparently do not care about sharing data with you, or with the group. In such case you do not need to bother sharing your data with them either.

Otherwise, you could also use the feature "Authorized Viewer" with some very close friends or you physician. It is above both standard sharing levels, and it offers little bit more than just the activities:

Garmin Connect App: Sharing Your Garmin Connect Account | Garmin Customer Support