Are you...
The internet?
I connect people with each other.
The internet connects people from around the world
I am open for everyone
Anyone with access to it can use it freely
and though, at the same time, only few can get access.
Not everyone can afford internet access
It's good to have me... let's you be more relaxed.
Through the internet you can do all sorts of relaxing activities, such as chatting, listening to music, playing games, etc.
You can use me to get private with someone
You can have private messages with people and not have them publicly available
If you get this private, nobody will know that you are you. Everybody will just see the other one.
One of the key aspects of the internet is anonymity
At the same time, I am the endpoint of this privateness.
People who expose themselves on the internet basically give up their private lives to the rest of the world.
I don't have to be there physically, though I can.
You can connect wirelessly or via cables
My life consists out of rules - but I am made for them.
Internet protocols?