That’s the whole idea of herd immunity. Sometimes vaccines don’t work. For example, the flu vaccine is less effective in the elderly. However it’s recommended to get it. And less people that get the flu, the less it spreads.
But when people stop getting vaccines, you start getter outbreaks again. So yes your unvaccinated child can affect others.
Your child can spread chicken pox to an immunocompromised individual or to someone for whom the vaccine didn’t work.
You are ruining the concept of herd immunity because you are not alone in your thinking. Others do the same.
I am a believer in herd immunity and it’s benefits. I understand vaccines are not without risk, but a world without vaccines would be tragic. So I expose my kids to vaccines knowing that it is make me the world they live in better.
Sometimes I think we have it too easy in America and people invent problems.