Mostly, I make sure to stay keenly aware of my own shortcomings so that I am more patient with others. It can be hard to see a friend order a cow-milk latte when almond or soy milk is available, knowing that the friend knows what dairy cows go through, how they mourn their babies, who have been carted off to veal crates so that we can steal their milk.
Because I am all too human, I don't always do the right thing, so how can I expect others to perform perfectly on the issues that are my top priority? I don't mean that we shouldn't try to do our best, but judgment and recrimination are such heavy weights. I find that accepting that we are all fallible lightens my load.
Some people feel that humans have a right to eat other animals but not to trash the earth. They may choose veganism because a vegan's ecological footprint is light, but once they are not invested in eating animals, they are more likely to be willing to learn the details of what happens to them. That learning will encourage compassionate people to stick with a plant-based diet.
Some of us seem to be born with a drive to try to make the world kinder. In my twenties, living in New York City, I worked in a soup kitchen every Sunday for many years, just trying to do my part. Then I read Animal Liberation and learned about factory farming and the killing of animals for oven cleaner and realized nobody needed my help as badly as the animals did.
When I see vegan food sold in single-use plastic containers, I get frustrated knowing that plastic is not really recycled; it is down-cycled to less and less reusable grades, and too much of it eventually ends up in the ocean - where it kills animals. Caring for animals means caring for the environment they live in, and vice versa.
Many people will first be attracted to veganism for their health but find themselves far more open to learning about the animal issues when they don't have to block them out three times a day in order to enjoy eating. Then once people learn, it is hard to forget and go back. Come for the body, stay for the soul.