Why won't my follower just leave me alone‽
Solution 1:
By habit, I have positioned my clickies on the right of my character, on the presumption that the companion would take a position on the left. This is the behavior of the pets in World of Warcraft.
A little experimentation shows that pets don't behave this way in StarWars TOR. When you change your position, companions path to the closest point on a half circle behind you.
o x o
* *
*z*
If they're coming from behind you, they are likely to stand right behind you(z) and obstruct your clicking.
If they're coming from in front of you, they'll choose one of the side positions(o), which might leave your clicking clear if the clicky is on the other side.
Just face your companion, and step back one tap.
If repositioning the companion this way doesn't work for you, another idea is to keybind the camera controls. ZoomIn, click, ZoomOut. I recommend F and V.
I do not recommend fighting in first-person cam (many effects do not appear, such as your own gunfire).
Solution 2:
I've found that increasing the max camera zoom (Located in the Preferences under Controls) to around 40% helps a lot with this. Being able to zoom out makes it much easier to click on what you mean to click on, and generally makes the game feel much less claustrophobic.