The preference alone is mostly harmless. When the preference is combined with the misapprehension that the preference can be fulfilled, it may harm the person asserting the preference if it leads them to make a bad choice between a meowing cat, a barking dog, or delaying the purchase of a pet.
If the preference order were (1. Barking Cat, 2. Barking Dog, 3. Meowing Cat, 4. No Pet), then the belief that a cat could be taught to bark could lead to the purchase/adoption of a meowing cat instead of the (preferred) barking dog.
Likewise, in the above preference order, or with 2 and 3 reversed, the belief in barking cats could also lead to the person delaying the selection of a pet due to the hope that a continued search would turn up a barking cat.
The problem is magnified, and more failure modes added, when we consider cases of group decision-making.
"I would like to have a cat, provided it barked" states that U(barking cat) > U(no cat) > U(nonbarking* cat). Preferring a meowing cat to no cat is a contradiction of what was stated. The issue you raise can still be seen with U(barking cat) > U(barking dog) > U(no pet) > U(nonbarking cat), however - a belief in the attainability of the barking cat may cause someone to delay the purchase of a barking dog that would make them happier.
*In common usage, I expect that we should restrict it from "any nonbarking cat" to "...
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