
Just for the record (lest people think me a monster) let me say that I have "owned", loved, and cared for pet animals all my life. From dogs and cats to fish and reptiles, they have been a great source of joy, education, companionship, and relaxation.
And as I've said here before, in my "libertarian" society boycotting and shunning people that
I consider to be "animal abusers" would be perfectly acceptable methods of discouraging what
I consider to be mistreatment. I could organize, lead, or participate in such shunnings and boycotts. In a my "libertarian" society, private businesses in the community would be free to refuse to serve these "animal abusers".

Imagine the result if the bank and the supermarket and and the gas station and the hospital (fill in the blanks) could turn away these "abusers"! Landlords could toss out "abusive" tennants! Schools (all private) could refuse to enroll the children of "abusers"! Garbage pick-up could be cancelled!

The potential pressure (non-violent and consistent with individual rights) could be quite successful (if they either change their ways or move away to face another community).

If unsuccesful, that would indicate a lack of community consensus as to the offensiveness of the "abuse". But those truly offended could continue with their efforts!
At the heart of the original question however, is whether or not "animals" have "rights", and if so
which "animals" and
which "rights". Can they be "owned?" What does it mean to ""own" a thing? Until those questions are answered persuasively and consistently, I do not think that being "offended" can trump the individuals right to "property." "One woman's pet is another woman's jacket!"

Then there's the variant of Ted Nugent's famous quote-"Must we kill it before we grill it?"

The debate continues...