Kathy and Shawn Lewis, of rural Alhambra, have adopted out about 35 horses through their non-profit organization, Legendary Mustang Sanctuary. Alhambra couple rescues mustangs and burros | Belleville News-Democrat
Actually yes, all of your Constitutional rights can be taken away. This is made possible by the 5th amendment. The little part there about nobody can be deprived of life, liberty or property without DUE PROCESS...that's what gives them that right.
Normally, you cannot invoke a right if you have a dispute between two private parties. For example, if a private company reveals person information about you, you can't sue them for infringing on your constitutional rights, since in the US constitutional rights involve only interactions between you and the government.