The first thing to realize is that some people aren't arguing, they're just screeching at you. Anyone who's honest and open will give you the benefit of the doubt if you can assure them you're thinking carefully about this and have some answers. Those people will be looking for flaws, though, so the best advice is to not speak poorly. (I can't put that into words; when I see some people speak, it's obvious they're missing some pieces, and that makes it easy for more 'normal' people to dismiss them as strange and wrong.) Keep in mind that group dynamics can keep people closed even if they would otherwise be more open, so it's rarely useful to speak to a whole group.
1. Anyone talking about consent is talking about something inherently human. I'd start there: legal consent is about the ability to be part of our social and legal structures. Animals don't worry about our social structure, and so they don't worry about their public image or feel general societal shame. This point is also where they like to conflate animals with children, so you can assure them these animals are fully-grown adults who will not be expected to integrate into society later. They won't have difficulties because of some new-found shame that they see in their past relationships. All of this is important and fairly intuitive for humans to think about with regard to other humans, but it just doesn't apply to animals.
From there, it's important to note that we're interested not in gaining some kind of invalid legal consent, but rather their assent. We seek their assent in many things, from training to play to choice of food. That's what animals need in order to avoid abuse. Most pet owners don't worry about their assent when altering their bodies with unnecessary surgery or locking them in kennels overnight. We think we'll be able to have some very important conversations about abuse once people realize we should consider their assent.
2. Some people think animals are soulless automatons, and I'm not sure you can convince them otherwise with some kind of argument. There's a huge industry in North America invested in de-sexing animals to keep them pure and simple and easy to think about, which is pretty disturbing to us. Adult animals will have sexual needs, and it's important for people to realize that it's entirely natural. There are a lot of people who have to come to terms with the idea that animals grow up and have sex. There are people who need to realize that their human sons and daughters have grown up and are having sex, and are more complete beings because of it. These people should spend less time worrying about visualizing others having sex in various ways.
It's important to realize that people probably block these thoughts because they don't want to think about animals who are abused for meat or dairy. It could be that people who think this way have a vested interest in not understanding animals, and being fine with their abuse. In that case, they're probably just angry at you for having weird sex. (See above.) A lot of these laws or moral laws, or specifically carve our exceptions for farming, so it's not like people are against the act itself. I don't think there's any way to argue the point, either. Don't tell these people about your sexual preferences, whatever those may be.
3. This is their weakest argument. You can assure them that any loving zoophile is taking on extra responsibility to read positive emotions in their partners' body language, and that we also look for the smallest negative reactions. It's our duty to constantly be checking for signs of discomfort, and to stop if so. As to the corollary: Many regular people aren't in tune with the needs of their pets, and cause abuse by neglecting them or feeding them improperly, or stuff like that. We're fighting for a world where people pay attention to their animals' needs.
In my eyes, ours is a righteous cause. We're arguing that we ought to care more about the wellbeing of animals; that we should be farming animals less, or not at all; that we should understand their place in the world as sentient beings with emotions. The one annoying bit is that we're driven underground by humanity's fear of sex.
