It’s absolutely not a normal thing to do for entities that want to use the “we are just infrastructure, our users are responsible for their actions” excuse.
In fact, such entities (e.g. power grid, telecom) are often legally prohibited from choosing their clients, and in exchange aren’t held responsible for what their clients do with their services.
So if you had a hammer in your yard, and somebody took it and misused it, you would not be responsible, but if you gave it to your neighbour and he used it to crush a skull, you the owner of the hammer would be responsible? It is clearly at least the opposite. Abstract from the "paid service", but see that.
The rule you propose (filtering would create responsibility) makes no sense. Try to show why it would be so, maybe.
No, with these limited elements. The filter may just be "of course I will not provide my (free) service to people that may use it in what I call a repugnant way".
When you know Harry is a rogue CEO, say a misinformation spreader or the issuer of unethical products, and you refuse to work for it, to provide it your services: does that make you an "activist"? Many people will call it "just the normal right thing to do". This is similar to people here calling certain positions "centrist" or "extremist" - and that entirely depends on how those positions are interpreted beyond their dumb (not telling) label, and on the dumb labels over said labels.