Anarchism has always made the point, correctly, that states exist to defend a minority of wealth and privilege against the majority of the community. They don't exist to provide necessary services to the majority: they only do this when the majority compels them, or when failure to do so imposes a cost that is unacceptably high. If you just tune out and let a government do its thing, like most of us do when we are preoccupied with trying to survive, you see lots more government for the rich and much "less government" for everybody else. That's happening right now, in fact.
When people understand this -- that government "represents" them only when it has no choice -- they are in a better position to influence their government -- and in the past they have. The achievements, like Social Security, unemployment benefits, and any other number of rights and freedoms, are at the same time 1) very important to people and 2) not bound to the point about the nature of government in any particular way. You might support them for the simple reason that no non-state substitutions yet exist to address those problems.
There are radical reasons for supporting moderate reforms when the proposed alternative is not yet plausible, as is the case when vulnerable populations, encompassing both majority and minority groups, retain more confidence in government solutions than non-government proposals. That most Americans associate "no government" with free-market capitalism or gang rule, instead of highly-organized societies liberated from coercive rule, is an indication that we have a lot more work to do before the point that governments defend the rich can be of greater immediacy than what is daily required to survive.