True story - I'm a member of the Vegan Costco Fb group and lots of people get the veggie pizza for the outside snack bar, sans cheese. Some people have actually had them refuse to make it without cheese - saying it's tto much work or something. Crazy!To me this is cut and dry. A vegan is someone who avoids eating all animal products. There's no doubt that your lifestyle eliminates a lot of harm, but that isn't the question. A 30 year Vegan will always have 25 years on the 5 year vegan. Even if they started eating animal products regularly they might claim to be "more vegan over all" if Veganism was some sort of scale. But since it's not, if the 30 year vegan starts eating animals in year 31, then out of the two only the 5 year vegan can make the claim truthfully.
You're a vegetarian with very few things to give up to be Vegan. Get rid of those weekly Gelatin candies, find bread and pastas that are egg/milk free (I've found many wholegrain ones are), refuse ice cream and other stuff when it's offered, and send the cheese pizzas back.*
* I have always disliked cheese even when I was a practicing omnivore and I have never had issue getting pizzas without cheese. One just has to be explicit when ordering: "no cheese whatsoever".