I think people talk more about negative externalities, which are fought through taxes, not encouraged through state support.

Much of what is encouraged through state support has nothing to do with externalities. For example, growing corn has no significant externalities, but it is heavily subsidized.

At any rate anyone who opposes central planing and "big government" also opposes capitalism in it's extant form.

In other words, if we oppose big government, we oppose the current government, because it's big? I think that's generally what people mean when they say they oppose big government, unless they're arguing with a communist that wants it even bigger.