valid.
Dog person is a loaded term I think. Most times a "dog person" is a person that just prefers dogs or has no particular animus towards cats and in general is an animal lover and cats are just not their bag.
Other times a "dog person" delights is talking about murdering feral cats, having their dogs murder cats, or just generally trying demean someone's choice of domestic animal companion. Then you've got the masculine/feminine implications that come along with the discussion, which is also childish but expected from a certain section of jugheaded motherfuckers. These are the people that can get fucked dry by a cane corso.
And yes, you will never see a "cat person" in the dog thread shitting all over anyone's choice of pet, or even critiquing it really. With the pitbull thread being the exception I suppose.
So yes your logic is sound. You are more like to encounter an "asshole" dog person, than an "asshole" cat person IMO.