Do cataracts cause strabismus?

Sometimes. Strabismus can be caused by deprivation of vision, such as from cataracts, retina disease, eye injury. The eyes tend to deviate outwards in adults. Often the eye will realign when vision is restored.
Rarely. Usually this only happens when the vision loss is very severe and has been there for months or years.
Indirectly they can. Cataracts are cloudy lenses; strabismus is misalignment of the eyes. Cataracts cannot misalign the eyes, but your brain requires equal and high-quality input from both eyes to focus the eyes together and keep them straight. Over time, blurred vision in one eye (e.g., cataract) more than the other may cause the blurred eye to drift (i.e., strabismus). Cataract surgery may reverse the strabismus.
It can! Dense cataracts that cause poor vision, may lead to brain loosing the image from the eye and therefore not be able to align the eyes anymore. This can be seen in elderly with long standing cataract or in children with dense cataract!