As others have noted, it's entirely possible to be a sprint athlete and be vegetarian, even at the highest levels of sport.
I think the biggest challenge comes with how much time, effort, and money are you willing to spend to get the same nutrients and dense calories that you can with a traditional athlete's diet.
I ran into this when I tried keto diets a few times, and keto is pretty simple. It just became really frustrating to eat out or constantly prepare my own food while needing extra calories because I was training so much. It felt like work, even in Portland, OR where it wasn't unheard of to order a "burger in a bun of lettuce". Doing that in Atlanta was that much more difficult.
That being said, most top athletes have generally regimented diets. But, us weekend-warriors, not so much.