Also, note that the comparison is about people who share cat or dog photos and their Facebook friends -- not about cat or dog people and their actual friends. I'm a dog person and many of my friends are cat people, but I wouldn't be interested in seeing their cat photos on Facebook. Nor would I be posting dog photos anywhere...
Cats don't particularly need exercise, are small, tend to be able to entertain themselves, and for whatever reason, are easier to get permission to have in apartments[1]. So if you're a city person, it's magnitudes easier to be a cat person, if you're going to have pets at all. City people are more liberal than country people, on average.
[1] I cannot stand litterboxes, hairballs, or cat urine, so this baffles me...
Regardless, I can't really give anything but my counter intuition; I wish I had the data Facebook has.
Despite the 'crazy cat lady' stereotype. Cats are preferred pet for men in the past couple of years.
http://www.businessinsider.com.au/republicans-dog-people-dem...
Where I live, it's definitely not true... or men at least don't admit to preferring cats.
If you did an a survey of men in Dearborn, Michigan you would probably find the opposite, with significantly more men preferring cats (due to religious or cultural reasons)