The general claim people make suggesting things like Right To Be Forgotten or Right To Privacy is that it violates "free speech", and particularly, that via Citizens United, the US currently claims corporations have the right of free speech. Google believes, for instance, all limitations on how it provides search results as an infringement on Google's right to "say" whatever they want.

Of course, we already have a variety of limitations on free speech, plenty of laws that restrict what companies and and cannot disclose about other entities, and GDPR would be no different.