Rythim

There is a trick you can learn to help with that. If you know which eye you are seeing with you can look slightly to the left or right of the person so that it looks like both your eyes are about even. Also, depending on the angle of your eye turn you can ask an optometrist to prescribe a cosmetic prism lens which will make your eyes appear to be looking more straight.

Having stereovision is no big deal. It comes in handy for fine detail things like catching a ball or sewing, but as you said for the major things it doesn't make a big difference. It makes no difference at all for tv and books because those things are flat anyway. If I close my eyes I don't feel like I see any different but I will still over reach or knock things over. So it's more of a subconscious thing that makes me less clumsy.

The reason why eye surgery does not fix your problem is because controlling your eyes are way complex and a simple surgery won't teach you how to use your eyes together well. Interesting fact, strabismus (eye turn) is not caused by weak muscles but by the inability to properly control those muscles. It's like doing piano exercises. Though they are called exercises they aren't about making your fingers stronger. They are about learning how to control your fingers to play quickly and accurately. Just as finger surgery won't make you a great piano player, eye surgery won't teach your brain how to control your eyes. I definitely recommend vision therapy. I worked in a vision therapy practice for a while and it really helps a lot. Even if you don't get stereovision at the very least you can learn how to keep your eyes straight while talking to people.

Not to be rude but to be technical you do have depth perception. You wouldn't be able to drive or even walk without it. What you lack is stereovision, which is the fine detail depth perception using two eyes together give you. And to be honest I think you still have stereovision you are just not aware of it until your presented with the over exaggerated effect that 3D movies have. It's the same for me, the world doesn't look bubbly and in your face like 3d movies but I don't have a problem with picking up objects and pass the stereovision test.