The best way to answer this question is to start thinking about what it means for a war to “involve” someone. For example, we now have troops fighting to some degree in Afghanistan and had troops involved until a few years ago in fighting in Iraq. Were you “involved” in that war? Why or why not? Now let us think about this with respect to the Civil War.
The most obvious way for someone to be “involved” in a war is to be in the military. It is said that 3 million men were in the military on both sides in this war. This was about 10% of the population. So we know that at least 10% were actively involved in the war.
Then there were people who worked in support services. These were people like nurses and others who were working directly to help soldiers. We do not have numbers for these people, though there surely must have been many of them. They would have been fairly directly involved.
Next, we can think of all the people who had loved ones who were directly involved in the war. If 10% of the entire population was in the military, the number of people who knew someone in uniform must have been huge.
Next, we can think of all the people who lived in places where the war was fought. Much of the North was spared this problem, but fighting raged through much of the South. This would have caused huge numbers of people to become “involved” in the war.
Finally, we can think of all the people whose lives were affected by the war. Surely almost all slaves felt “involved” in the war, hoping that the North would win and they would become free. Surely, most of the South felt some trepidation about what would happen if the North won. Were these people “involved?” What about all the people in New York City who were affected by the draft riots?
If I were answering this question, I would try to think about what I think it means to be “involved” in a war. I would probably conclude that the vast majority of Americans were involved in the war to some degree. I would try to lay out various levels of involvement just as I have in this answer and I would try to think about how many people were likely involved at each level.