do I have a right to legally have your cats removed so that I can enter your home, which you so graciously invited me to do?

No.

But if you engage in activities that cause me harm when I am not on your property (like dumping toxic waste in your backyard that contaminates my drinking water supply, or playing music so loud that it disturbs me in my own home down the street, or keeping noisy/vicious dogs that get loose and endanger my safety, etc.) then I have a right to complain.

I guess it comes down to this: you can do whatever you like on your own property, as long as your actions do not endanger people who are not on your property. To carry the example to a ludicrous extreme, you may well be entitled to own your own bazooka so you can do target practice in your back yard. But if those rockets escape the confines of your property, then that would not be acceptable.

tanstaafl.