Even getting home insurance to begin with often requires an assessor come out - who looks at everything about the building and property and what's on it. Getting it renewed, same. They can refuse coverage for owning a pool, certain dog breeds, certain types of out buildings - whatever. The reasoning for some of these is that it might draw people in, they'd get hurt and then the insurance would be paying out.
This is a crappy situation, but you're not going to manage to hide something the size of Burms. Balls and frozen in the freezer, sure, maybe. Brums and a building full of rats? Ain't no way.