I think it’s difficult to place them in one category or the other because the definitions of blue collar and white collar are becoming increasingly muddled over time. While it’s true that the term “blue collar” traditionally referred to those in manufacturing and in trades, the US has comparatively few manufacturing jobs left, and traditional “blue collar” type jobs don’t occupy a whole lot of the labor force. We used to group people based on whether their job was white collar, blue collar, or an unskilled laborer position. Now though the terms white collar and blue collar are often used to differentiate between people with formal education, like computer programmers, and people without it, like call center workers. So with the watering down of the terms, it’s easy to argue that pilots kind of ride the line between the two: their profession doesn’t categorically necessitate formal education (one can be a pilot with only a high school degree), but they’re also not unskilled laborers.
But I would agree with Rick's point that pilots are professionals because of their high level of training and responsibility. Although flight school bears more resemblance to an electrician's trade school than it bears to law school, I think the level of professional responsibility that pilots have bears more resemblance to other "professional" positions than it bears to an electrician.