The first thing to say here is that even if the story Conard is telling is true, it's true because women and non-white workers make a whole let less than white male workers, which is not exactly a heartening economic datum. The bigger problem is that Conard is using bad numbers and the story he's telling is just wrong all around.
The first problem is that, as Lane Kenworthy notes, racial minorities and women were being integrated into the work force well before median wages started to stagnate in the 1970s. Indeed, white men's share of the workforce has declined at roughly the same speed since the 1950s. This means something else likely caused wages to stagnate and that simply continuing to integrate women and racial minorities isn't the cause.
The second and bigger problem is that Conard's central contention - that wages have increased for each gender and racial group - is simply false. As Evan Soltas notes, just looking at Census data it's clear that income for men, and non-Hispanic white men particularly, has stagnated.
But it's actually worse than that. The best recent work on changes in male wages has been done by Michael Greenstone and Adam Looney of the Hamilton Project, and they have found (pdf) that median earnings for men have actually declined since 1969:
As you can see on the black line in the above graph, median earnings for men in 2009 were lower than they were in the early 1970s. And it gets worse. The decline shown above is actually too mild, because it doesn't take into account the massive exodus from the workforce of men since that period. Between 1960 and 2009, the share of men working fulltime fell from 83 percent to 66 percent, and the share not making formal wages tripled from 6 percent to 18 percent. When you take all men, not just those working fulltime, into account, the slight decline in the above graph becomes a plummet of 28 percent in median real wages from 1969 to 2009.
Greenstone and Looney also note that this decline is not due to a larger number of men retiring early, as the decline is the same if you only look at men ages 30 to 50, none of whom are likely to have retired yet. Most troubling, the change is more dramatic the less education a person has.
High school dropouts' earnings have fallen 66 percent since 1969, and people with some college - the median level of education in the US - have seen earnings fall by a third. Reasonable people can disagree about what caused this massive decline and what should be done to fix it. But it's a major crisis and people like Conard who deny its existence are just wrong.