I feel that a layperson must be politically engaged to do their proper duties to family and to community. It’s one of the “pains” of being a layperson, especially if you live in a democratic society. Government service is seen as a legitimate trade in the Dīghajāṇu Sutta (AN 8.54) which you could easily see as being a bureaucrat or working in some kind of socially engaged programming, or and Non-Governmental Organization (NGO) that serves in a similar manner to a government position. I don’t know if it can count as being an elected official, it probably depends on the position.
As for being politically engaged as a layperson who isn’t working for government I feel like it’s a social obligation in a democratic or semi-democratic society. If your voice can matter then you should make it count. The Dīghajāṇu Sutta and the “Childless (1st)” (SN 3.19) both at least mention rulers as ones who can take your money and that it’s not the best thing,
When a bad person has acquired exceptional wealth they don’t make themselves happy and pleased. Nor do they make their mother and father, partners and children, bondservants, workers, and staff, and friends and colleagues happy and pleased. And they don’t establish an uplifting religious donation for ascetics and brahmins that’s conducive to heaven, ripens in happiness, and leads to heaven. Because they haven’t made proper use of that wealth, rulers or bandits take it, or fire consumes it, or flood sweeps it away, or unloved heirs take it. Since that wealth is not properly utilized, it’s wasted, not used.
Your vote can influence policies put in place that can help or hurt your livelihood. So this is doing your duty according to Sigālaka Sutta (DN31) since you should honor one should support their family and friends according to the six quarters. They are not all social obligations but some financial too. This isn’t to say that someone should hoard their wealth for themselves, their family and friends though because this would go against generosity as described throughout the Pali Canon. You can see it also in the Dīghajāṇu Sutta and in The People of the Bamboo Gate (SN 55.7) where the virtue is praised in general terms and not just to monastics.
This likely means that if someone can socio-politically engage to protect or improve their livelihood and family, or as an act of generosity then they should do it. Of course one should be mindful while being engaged in politics,
You should distinguish two kinds of people: those you should associate with, and those you shouldn’t associate with.’ That’s what I said, but why did I say it? Take a person of whom you know this: ‘When I associate with this person, unskillful qualities grow, and skillful qualities decline. And the necessities of life that a renunciate requires—robes, alms-food, lodgings, and medicines and supplies for the sick—are hard to come by. And the goal of the ascetic life for which I went forth from the lay life to homelessness is not being fully developed.’ In this case you should leave that person at that very time of the day or night, without asking. You shouldn’t follow them.
from Association (AN 9.6)
Like most things it’s a balance between action and inaction, or engagement and disengagement, and we shouldn’t be attached to any result we get from those actions and deal with whatever hand we’re dealt as it comes along.