It turns out that stereovision is the least important of several depth cues humans use, and is only really effective out maybe 10 feet or so--beyond that the parallax is too small to give much useful info, and we rely on apparent size, relative motion, surrounding context, etc. I can catch a ball just fine, as an adult.
It's really only an issue within arm's reach, and then only when I'm distracted. Occasionally I'll reach for something without paying attention and miss by, like, a foot. Also, I can't use 3D glasses. (With the new polarized kind I can at least wear them and see a normal 2D movie. With the old red/blue kind, everything would be either red or blue, depending on which eye I was using.)
You might have an advantage with not being able to watch some 3D movies - you can tell your friends/family that a medical condition prevents you going to them.
I have comparatively uninteresting/normal vision (biggest issue shortsightedness) but I have this too. My left eye sees more blue, my right eye more red. Looks like the cone distribution wasn't perfect.
I'm not sure, but I think the sun's rays don't have much of a blue component: my left eye gets fractionally less sore from bright sunlight, so if it's really bright out I'll generally be closing my right eye.
Once I got the new glasses I was astonished at how flat and "PlayStation-like" everything looked. My depth perception was thrown off and everything looked much closer to me than it actually was.
I think my brain was using blurriness as an indicator of depth, in addition to binocular vision, and with my myopia corrected it lost that information and had to readjust to relying primarily on binocular vision to gauge depth.
When I was in college I was fairly decent on the ping pong table, call it high amateur. I also have very very bad vision - -5 diopters in one eye and -6 in the other. At the time I wore contacts and I was also really really poor. At some point I lost one of my contacts and for six months I was effectively blind in one eye for the purposes of ping pong. It took me about a month, but fairly quickly I was playing at my old level without anything close to stereo vision.