Can you have strabismus without your vision being affected?

Yes: Longstanding strabismus is usually compensated for by the brain which uses only one eye at a time, suppressing double vision.

Strabismus: Yes. Some people with strabismus have double vision and reduced stereo vision (depth perception). Many people with strabismus see very well-- they do not have double vision and their eyes work together well. It is simply a matter of degree, since the brain can compensate for small amounts of strabismus. See you local eye doctor if you are having double vision or trouble focusing.

Yes: If you have alternate vision meaning that you see with one eye at a time this way one does not develop a lazy eye.