Though America tends to emphasize freedom, there are two groups you need to watch out for: religious and animal rights. Though you'd think animal rights groups would help, they can be a bit extreme.

Don't be stupid. Close your blinds and don't do anything questionable out in public.

https://en.wikipedia.org/wiki/Zoophilia_and_the_law_in_the_United_States

Though it is frowned upon, Americans do have a good sense of humor about the stuff.

The United States is not a safe place (legally) for zoos. As has been said elsewhere, consider the fact that 5 states have anti-zoo bills right now (Texas, Kentucky, West Virginia, Nevada and Vermont), and that many states (such as Ohio) recently banned sex with animals. Also consider the fact that even in states that have no laws specifically prohibiting sex with animals, people have been charged with (and convicted of) "animal cruelty". Also remember that the U.S. has the world's highest incarceration rate.

Excluding the states with bills, that would leave only 3 states (Wyoming, New Mexico and Hawaii) where it is legal, plus several U.S. territories and DC.

Latin America may be safer, though even there there's still risk (for example, Brazil criminalized sex with animals in 2015). Depending on the country, it may (or may not) be safer.

I don't think there really is any safe place for that.
Once found out, they can use so many excuses."Where's the evidence that the animal hasn't been raped?" or something along the lines of that.
They don't care about psychological harm, they'll ask for the animal's consent and of course, they can't talk with our language.
But that's just an example.
And it's not like kissing your partner in public will result in an 'awww' but rather an 'ewww,' so it's not going to make a big difference anyways imo.
So I recommend not bothering with any of this at all.

My advice would be a sort of compromise: look for states where sex with animals is not a recent concern and where it isn't a felony or given a ridiculous sentence. Wikipedia is a surprisingly accurate resource on this, and recently updated in light of pending legislation.

Ultimately, though, your actions are most important in avoiding a criminal record and social disgrace. Put simply, don't fencehop, don't publish videos or pictures of the act, and choose carefully who you tell about it if anyone, and being found out will be difficult. After all, it really doesn't affect anyone but you and your partner, and if you treat them with respect and kindness it shouldn't be anyone else's concern.

What difference does it honestly make about the law? Do laws stop people from racing on the street or from selling and using narcotics? Hell no and those are just two examples of laws that are willfully broken on a daily basis that have whole, organized sub-cultures devoted entirely to breaking the law.

As has been said, close the blinds, don't do anything stupid and forget about the laws that the puppets in office make.

I'll also make one other thing very clear. Think in terms of human/human relationships. What would you do if armed men burst into your house and tried to abduct and possibly murder your SO? For me, it's simple, I would gladly die defending my lover before I chose to cower in fear and live without her. She's given me her entire life and she has mine in return.

i am from wyoming and zoophilia is legal here