In no particular order, I expect you'd see some variation of the following:
1-Legislators in some large W. states would rush through legislation prohibiting the federal government from exercising eminent domain to seize public land for protection of Bigfoot, or limiting any lawful economic activity for the sake of their protection as well. Some other states would enact legislation to adopt BF as their state's official animal. All of your usual state v. federal power arguments would be trotted out in state capitals and in Washington, D.C. Gridlock (again and still) would ensue.
2-Amnesty International (or some similar human rigths advocacy organization) would immediately file an action in federal court to enjoin the further killing, torture, enslavement or harrassment of BF. A ruling in their favor by a federal District Court judge (affirmed by a Circuit Court of Appealsl) exacerbates the situation posed by 1., above. The SCOTUS decides by a narrow majority that a BF is entitled to equal protection and rights granted by the 13th and 14th Amendments, and there exists no rational basis for states to deny these rights to them. Rick Dyer, a self-proclaimed spokesman for BF (and who submitted an amicus brief on their behalf), takes it on himself to go to the woods and read the opinion outloud, with Scott Nelson translating for him. FBFB films it in its entirety and supplies red lines and circles for the edification of the Justices.
3-Dr. Jeff Meldrum starts his second career as an expert witness, and half the faculty of ISU calls in sick that next work day.
4-Bigfoots everywhere continue not to care.