That's a tricky question because modern progressive political views are opposed to religion. And religion is a large source of irrationality. So most examples are going to happen to match modern progressive political views just because of that, even though they're not measured by their agreement with modern progressive political views.
The first example that comes to mind is a decline in anti-Semitism. Anti-Semitism 1) is irrational and 2) because of left-wing opposition to Israel and the West and support of third world Arab states, is not necessarily reduced by modern progressive political views.
Another example is how a lot more people have realized that central planning doesn't work. An example where things have become less rational since the 1900's is the current irrational belief that race and gender don't correlate with anything significant.
Suppose I told you that I knew for a fact that the following statements were true:
You’d think I was crazy, right?
Now suppose it were the year 1901, and you had to choose between believing those statements I have just offered, and believing statements like the following:
Based on a comment of Robin Hanson’s: “I wonder if one could describe in enough detail a fictional story of an alternative reality, a reality that our ancestors could not distinguish from the truth, in order to make it very clear how surprising the truth turned out to be.”1
1Source: http://lesswrong.com/lw/j0/making_history_available/ewg.