"Net Neutrality" has nothing to do with censorship or copyright infringement. It is who gets better network performance in return for extra payment, or with NN, that everyone is on a level playing field.
You don't say where you are located, so I can't tell you what your government can or cannot order you to take down. Lunarpages is in the USA, so there is a very high bar for taking down offensive material. If you are infringing someone's copyright or trademark, they can complain to Lunarpages and have your material removed. It's best to get permission beforehand to post material owned by someone else.
The same rules apply to FB, TW, GOOGLE so they can be ordered to remove infringing copyrighted or trademarked material. I have seen search results on Google that indicate one or more results were suppressed due to a copyright infringement complaint.