Unfortunately, past Star Trek series have not spent much time on discussing the plight of civilians during times of war (or even peace, for that matter), but we do have a few clues about Federation citizens during war:
The Maquis is probably the biggest, and best, example of a civilian population affected by a war (specifically, the Cardassian War). We don't see them during war itself, but rather in the aftermath, when the Federation-Cardassia borders are redrawn. As a result, a number of civilians living on previously Federation planets are forced to relocate to a new world, now that their planet has been handed over to Cardassia. Clearly, from the various episodes we see in TNG and DS9, the citizens forced to relocate are quite unhappy about it, forming an independent entity (nation, terrorist organization, whatever you choose to call it) - the Maquis. So there is obviously at least one portion of the Federation population that resents war.
Edit: From the discussion in the comments, I ralized I was mistaken - the Maquis don't really resent war, since they were partially responsible for the Federation-Cardassia war, and were quite violent in every episode we saw them in. Regardless, the peace treaty at the end of the war was not taken well by the Maquis, so I suppose it was the end of the war which the Maquis resented.
We've also seen glimpses of how those living on Earth tend to react to wars, or conflict in general. Specifically, during DS9: Homefront, we see that most of the residents of Earth are quite jittery - Joseph Sisko comments he has not seen people so nervous since the incident with the Borg (the Battle of Wolf 359) - another hint that citizens of the Federation get quite nervous and worried when Earth faces a conflict. (it is important to note, however, that Joseph Sisko himself is relatively calm about the situation, implying that there are probably a number of Federation citizens who pay less attention to the war unless it actually directly affects them.
Although we did not see much of Harry Mudd in the Original Series, he will return in Star Trek: Discovery, whose first season is set during the Federation-Klingon war. This is pure speculation, but from the season's trailer, it appears that Discovery will explore the impact of war on civilians through Harry Mudd (who will first appear on tonight's episode, "Choose Your Pain"). This should prove to be another insight into the relation between Federation Citizens and Starfleet (essentially its military, among other things).
Edit: I watched "Choose Your Pain", where we find Mudd onboard a Klingon prison vessel.
Mudd is joined by Captain Lorca, who has been taken prisoner, and goes on to have a discussion with Lorca about his ideas on war. Mudd clearly hates the Federation's war, saying that it takes a huge toll on "the little guys" and that they're "sick and tired of being caught in [the war's] crossfire".