The provision of an Internet connection is not a moral question. An Internet connection is a collection of standards interoperating such that your house can connect to the Internet and access content. Your Internet Service Provider (ISP) doesn’t push content through the connecting wires, fibres or radio waves; rather it is a passive connection that waits for something inside your house to request something; it’s a pull, not a push.
You have to wonder if the traditional referencing among the ISP community to "pipes" as a collective term to describe Internet connections has caused people (politicians and some of the media in particular) to see an analogy with mains water. Mains water is not just delivered to your premises, but delivered to a certain chemical standard, to a level of purity. But is also delivered under pressure; in the house people can only restrict or block it, they cannot change it, cannot increase the flow rate or pressure, and they don’t have to do anything to ask water to come from a certain tap; they open the tap, removing what was holding back the water, and in the water comes. Moreover you cannot choose to get your water from different sources, per tap or per tap open. Water is a pushed service.
Your Internet connection on the other hand is far more similar to electricity; like electricity an Internet connection does nothing further unless you or someone in your household actively requests that it does. With electricity that’s when you plug in/turn on an electrical item like a TV, kettle or drill; with an Internet connection it’s when something connected to your house wifi network tries to go on the Internet. Until you turn on the kettle, no electricity is used by it, whether or not the socket is turned on, and the kettle will use exactly the amount of electricity it needs to boil the water in it. Electricity is a pulled service.
Likewise until someone in your house starts a web browser no content enters your Internet connection, and only the content requested by that web browser passes to and through your Internet connection. Different browsers in your house, on tablets, PCs and TVs, can request and receive different content and different content types (images, videos, text, etc.) from anywhere in the world all at the same time. But if you cut the cable to your router nothing will come out; try that with your water pipes and you would have a powerful illustration of the difference between water pipes and Internet connections.
Asking the ISPs be responsible for what content you request is like asking electricity companies to be responsible for what is done with the electricity you use. They both just provide dumb wires through which households and businesses pull what they want; only water companies push stuff at you through pipes.