The teleporters follow the same rules as normal teleportation. You cannot travel if:
1. You're in heat of battle
2. Flagged criminal
3. Your character's weight exceed his capacity
4. You are dragging items
5. You aren't allowed access to that facet (reds in Tram, Youngs in Fel, no entitlement)
6. You aren't allowed access to the destination house
So if you are friended to Player A's house that has a teleporter to Player B's house, but Player B's house is private and you're not friended to it, you will not be able to teleport into Player B's house from Player A's teleporter. But if both houses are public, and the start teleporter is at a security setting to which you are allowed, you will be able to travel back and forth.
*hopes that explanation was clear*