In my opinion, the one drop rule is finally beginning to lose some of its power, though it is by no means dead yet. That's because it is no longer acceptable to make official or legal distinctions between individuals based entirely on ethnicity. Plus, with modern DNA testing, many people who have always thought of themselves as "white" are finding that they do have some African ancestry. Those people will continue to consider themselves white, even when they find out about that "one drop."
However, I think the one drop rule is being replaced, for many in our society, by what might be called the "one shade rule" based on a person's visual appearance. In other words, if a person's coloration, facial features, or even their hair seems to imply any degree of African ancestry, they will be classified by some as being black, and will often be treated differently than if they were classified as white.
Although making such distinctions is, as you say, pretty silly, it still is, unfortunately, a reality we continue to live with today.