Cache causes webp images to not show

I spent a lot of time trying to figure out what was causing some images to not show as webp. I thought it might have been my lazy loader, but finally I realized that it’s CloudFlare cache and my server cache causing it. If I disable both then all images always display as webp. I excluded png, gif, and jpgs from CloudFlare and now it only happens when my server cache is enabled. I can exclude these files from my server cache so it never happens, but is this the correct way to resolve this issue? It seems like if cache causes this issue, a lot of people would have it since using cache is very common.