Yes, it is. There is quite the leap from "preferring your own" to lying about a specific group are doing something morally objectionable, in order to reinforce your campaign's anti-immigration messaging, though.
And yes, it is racist to lie about a group of people you don't like to make them sound worse so that other people don't like them too.
Like it was racist when Nazis said that Jews control the world and ate children and whatever nonsense you can think of.
Targeting a specific group of people's immutable characteristics to slander them to paint them negatively fits your "original" definition of racism. The couch fucker treated them differently, by lying that they specifically are eating pets.