They have to have internet service. Parler Ceo Matze said they were having troubles. I don’t know if they will be back up as they said.
If you have your own servers, it is much much more difficult to deny service, because no one is hosting anything. You are simply asking the provider (Verizon, Comcast, etc) to run a wire to your location. If they deny service it opens up a huge can of worms. This was all worked out a hundred years ago when US government tried to hold Bell Telephone responsible for gangsters using phones to plan crimes.