One might argue your job is to do what’s best for the child despite your beliefs.
And sure, the risks are lower for vegetarians but you’re still depriving a young child in your care of nutrition because of something you chose for yourself.
You seem to equate your diet with religion or some other deep rooted belief that you feel obligated to pass down. While the people who heard you were forcing this upon a child were thinking it’s more like choosing to smoke or drink heavily. Those two camps aren’t going to find common ground.