For female animals make sure you are as clean as possible. Thoroughly wash your hands and dick before each session, and if you opt to use soap make sure all soap is thoroughly rinsed/washed off as well. (Many soaps contain harsh chemicals which can potentially cause irritation.) I usually just hop in the shower before sexy time begins. Make sure your girl is large enough to accommodate you. I know many guys (including myself) love really tight sex, but if she's too small, or not stretched enough you can cause pain, chafing, and general irritation even with plenty of water based lube. Also, make sure you do not go overboard with lube. Too much lube can throw off her pH balance which can potentially lead to an increased risk for bacterial infections... but we're talking about a LOT of lube to cause that problem. Also, make sure your lube is water-based and not petroleum based.
Generally, it is safe to cum inside your animal. But watch your diet, I've learned the hard way when I was on a very garlic intensive diet. I don't think my girl got an infection but I had to stop all sex for 6 days because her coochy was starting to smell especially foul. Lastly, once you cum inside your female animal it's important that she goes pee shortly afterwards, this will help reduce the chances of a UTI.
And for course for your animal's mental health and well being, if she looks uncomfortable, always terminate sex immediately.