Exaggerated and made up example of what I’m curious about:
My country has legitimate elections. When my government wrongly convicts someone I feel as if I have personally wronged that person by voting for the person who appointed the judge. God will judge both me and the judge for it.
Somewhat but keep in mind that most countries that allow voting are not completely democratic. The actions of the government only consider the will of the people—they are not typically controlled by the people directly, though some are closer than others to this ideal.
For me personally it’s more about what actions can I take to influence the outcome? If it’s an important issue, am I doing all I can to exercise my voice? For the important issues this can go beyond voting. But if the government does something I don’t support and had no ability to prevent, no I don’t necessarily feel guilty about that.