It would be entirely possible to write campaign finance laws so that organizations like the EFF can only be funded by private donations and not by corporations,

It would be entirely possible to write campaign finance laws so that organizations like the EFF can only be funded by private donations and not by corporations, if they want to make campaign contributions or run "issue" advertising. I don't really see what unintended consequences you're referring to. The problem with getting corporate money out of politics is that the people getting it wouldn't like that, not that the law would be difficult to craft in a fair way.