You Decide Should People Be Allowed to Keep Exotic Animals as House Pets? Published October 19, 2011 FoxNews.com Facebook0 Twitter0 livefyre Email Print Should individuals be allowed to own exotic animals as house pets? Share your thoughts, answer our question then click "Leave a Comment." Should individuals be allowed to own exotic animals or should they only be housed in zoos or other similar insititutions? This is a non-scientific viewer question.