Not quite.
While the Bill of Rights originally was just limits on the federal government, after the 14th Amendment, the Bill of Rights became the means of discerning what important individual rights were.
So after the Bill of Rights were "incorporated" by the 14th amendment, they now are individual rights to be defended from abuse by stated, cities, employers, etc.
And your initial premise is also wrong because the Internet is federal, so all providers are supposed to follow FCC rules on not discriminating against political beliefs.