base URL has absolutely nothing to do with structured data, its only used for relative paths. I think you need to speak with Google about this... the base URL and your "unspecified type" really have zero relationship. I think this is a bug in their validator and you are thinking your will penalized, but I highly doubt you would be, again it has nothing to do with structured data.
Anyway, you can remove the base meta tag, but you would need to ensure you are using absolute paths when loading images and other assets in your template files. Personally, I don't think its worth it.