Sometimes it can sound odd, but it's meant not to distinguish between men and women in the context of the article's content, but to help female readers feel included. Decades ago, the convention in English was the one that came off as patriarchal. All writers just referred generically to "men" when they meant "people in general." That, too, would sound odd today, especially to nonsexists. So there's no great solution to this problem in English. Yes, you can speak in the plural, referring to "them" and "they." But you're also supposed to keep it singular in most cases.

Anyway, I'm obviously not implying that most conservatives are female. I'm using "her" rather than "him" to speak of conservative people.