I agree that intent matters, but insofar as a state governs with the consent of a majority (leaving aside questions of whether that consent is real), then taxation (incl. the level of taxation and its distribution e.g. welfare vs warfare) represents a broadly agreed mechanism of the state to provide the kind of safety net that OP described as levels 2 and 1.
Personally, I live in such a state (not the US), that has a safety net, and am happy to contribute via taxation. Not all my fellow citizens are happy to contribute and I accept that. I earn a decent wage and don't jump through hoops to minimise my tax. At the end of the day, people vote for governments that are more or less taxing.
IMO then the people happy to contribute to such a system would mostly fall under 1/2 (under the assumption that one's motivations are altruistic and not centered on the communal benefits they also receive), but the people who aren't happy to contribute would not qualify (at least, not via their taxes alone -- there might be other reasons for rejecting taxes, and they might contribute elsewhere in a way that still puts them in the 1/2 category).
Personally, I live in such a state (not the US), that has a safety net, and am happy to contribute via taxation. Not all my fellow citizens are happy to contribute and I accept that. I earn a decent wage and don't jump through hoops to minimise my tax. At the end of the day, people vote for governments that are more or less taxing.