You don't have to be vegan to like the BFG. I went with my nonvegan husband and we both enjoyed it. He didn't even catch the animal rights theme until I pointed it out.
BFG is the story of the friendship between a human girl, Sophie, and the Big Friendly Giant. She's the only human in giant country and he's the only one of his kind that doesn't eat humans. If she strays outside of his home she'll be considered nothing more than food. For the BFG, it's how it must feel to have an animal companion who's a pig, goat, chicken, or other animal that people traditionally eat.
The BFG is pretty explicitly a vegetarian. He exclusively eats the loathsome vegetable snozzcumber and drinks a fizzy drink called frobscottle. Later we see him among human beings where he revels in their varied diet, but we only see him eating vegetarian foods. Not vegan, alas, as we do see him eating eggs. Based on Roald Dahl's other works, I don't think the BFG's vegetarianism is an accident. It's part of the theme.
The other giants don't take kindly to his vegetarianism, calling him an insult to giantkind. If you were to catch a vegan on a bad day, the contrast between the other giants and the BFG would be like their list of complaints or accusations against fellow humans. If the movie is an animal rights analogy, deliberately or accidentally, it's not a favorable one and doesn't pull punches. The giants are unsophisticated. They don't speak as well as the BFG and probably can't read. They don't sleep indoors or have dwellings and haven't tamed fire, so they are literally uncivilized. They seem superstitious and fear the rain and water. Their diet has no variety - they exclusively eat uncooked human beings, though on this count, they're equal to the BFG who also has a mono-diet. They loathe vegetables. He's the only one actively trying to make the world a better place while the others lay about, play cruel games, and in general seem only concerned about themselves and their amusements. They are nasty and brutish. They're killers. They're happy to kill sentient individuals who aren't members of their own species, and they're quick to bully the only member of their species that doesn't participate.
To the other giants he's known as Runt, but the name he chooses for himself is Big Friendly Giant. His self identity is based around his compassion, whereas the other giants have names like Fleshlumpeater, Bloodbottler, and Meatdripper. If their names are self-chosen, and the have no parents to have given them names, they seem to identify with their appetites and the hunt.
Notably they are stronger than the BFG and outnumber him 9-to-1. He feels helpless to protect human beings from them. The only thing he can do is not participate in their hunts, protect a human being within his house, and try to entice the other giants into trying vegetables. Vegans are outnumbered 99-to-1, a factor of ten greater than the BFG. We all know what it's like to fight the same unpopular battle to protect our other-species friends from the appetites of our fellows. We know what it's like to try to share kinder food with them.
Thankfully we have quite a bit more than snozzcumber available to us. But the BFG is so committed to not harming humans that he's willing to live exclusively on the noxious vegetable, presumably for centuries, before humans gift him seeds for other vegetables to plant in his garden.
For all of this, the BFG cares about his fellows and doesn't want to bring them trouble. This is also the story of him learning to stand up for himself and take a stand against the other giants' killing. He does so not out of self-interest, and not out of principle, but out of love for Sophie who's put directly in danger by the others. I think most vegans, and most activists in general, can relate to loving people while absolutely hating what they unthinkingly do to others.
It took most of the movie for me to not feel I was looking at CGI characters. It was excellent CGI but the giants were clearly not physical actors. The BFG himself was the best done and his face was wonderfully expressive. His face was a version of the actor's face who played him. There were other CGI elements that I won't describe here, but which were shiny and delightful. The landscape of giant country and the trip to get there were breathtaking.
The film managed to be dark and adorable at the same time. That's not surprising since Roald Dahl also wrote Charlie and the Chocolate Factory, The Witches, and Matilda. I did feel that it lacked a certain sense of wonder that Spielberg films often have. As Richard Roeper said, giant country mostly seemed like a drag. But I don't think that was really the point. This wasn't Harry Potter where the main character is brought into a world that's both spectacular and dangerous. This is the story of a place that's dreary, boring, and brutish. It's the story of trying to make that world a better place.