Meatless: you can definitely leave out the ground beef for a meatless soup.
Tomatoes: I prefer an ultra-smooth consistency to the soup, so I run the crushed tomatoes through a blender before using (but that isn't necessary if you're fine with some "tomato-y" texture). Different brands of crushed tomatoes vary in texture.
Acidity: UPDATE since different brands of canned tomatoes can vary greatly in flavor (as you can see from the comments), adding a teaspoon or two of brown sugar can help cut the acidity.