> I do see some women who don't own dogs, and will say stuff in there about how much she loves them
That's the scenario I was referring to. For potential matches that already have pets of some kind, I usually see that they ask that the other person be OK with dogs/cats, which is very reasonable compared to "you must also have pets".
That's not at all what you wrote above. You said they were adding things like that just to sound good, not because they truly value it. You gave travel as an example, because you (correctly) assume many women put in their profiles that they like to travel, when in reality many probably only do it every year or two at best. This isn't the case with a dog: she must value it quite a bit to put up with living with it.
That's the scenario I was referring to. For potential matches that already have pets of some kind, I usually see that they ask that the other person be OK with dogs/cats, which is very reasonable compared to "you must also have pets".