Meat eaters can eat vegan food, vegans can't eat animal products in line with their beliefs. Providing a vegan menu means that everyone can eat.
Provide a vegan menu which anyone can eat; in that way, you are catering to all needs. Be aware of intolerances though; there are plant-based foods that will give me an extremely painful time, such as avocado, so be willing to take that into account for individuals.
Frankly, there is no reason why you should provide animal products to your guests. You are providing food that they can eat. If anyone is precious and self-centered enough to demand to eat meat or other animal products, then they are extremely rude and should get over themselves. They will not die from a single or even two meals without animal products. Would they demand that a Jewish or Muslim wedding provide them with pork as that's the only meat they eat?
If people say that they would not attend if you didn't provide meat, then these are people that you really don't need in your life. Who in the world would want to mix with such selfish, self-centered, ignorant, rude wastes of space and food? Be thankful that they have taken themselves out of your life. Those saying that on this thread have really shown themselves up. Anyone who attends your wedding should be there for your happiness.
I'm not a vegan but eat 90% veggie with occasional fish. The number of times that I have seen vegetarian or vegan options been eaten by meat-eaters because they think it is nicer than the meat dish, thus selfishly leaving others without food, is incredible. Many people have shared similar experiences on MN. I have taken vegetarian or vegan dishes to a shared meal without people immediately realising that there is no meat until they have thoroughly enjoyed it.
Pay no attention to the selfishness of others and provide a vegan feast that can be eaten by anyone, taking only allergies and intolerances into account. Congratulations and enjoy your wedding when it comes.