I tend to doubt, however, that this line of criticism will gain any traction, since making the argument requires you to say that IQ tests (which is all the AFQT really is) are an important measurement and most liberals prefer to shy away from the topic.
First of all the AFQT isn't really an IQ test, it's just used as a decent proxy for one because lots of people have taken it and have also put lots of demographic data with their scores so there's good data.
But I don't know these fantasy liberals who don't think that IQ tests don't measure anything. They measure something, certainly, and something we associate with "intelligence," no matter how imperfect a measure of a complicated thing they may be.
What liberals generally don't think is that IQ tests generally and the AFQT score specifically are a measure of "innate" intelligence, and certainly not a measure of genetically-drive-only-innate intelligence.
There's a very simple reason for this: you can teach people to improve their test scores, so it isn't a measure of innate or potential anything.
But I don't know anyone who think that such tests are meaningless. To the extent that low scores reflect low ability, low education, or whatever combination of those things, it's certainly a big deal that the military is letting in more "Category IV" scorers.
Just to illustrate rather easily, the AFQT score is derived from a subsample of the ASVAB test. One part which is used is "arithmetic reasoning" and another is "mathematical knowledge," both being things which most of us aren't born into this world knowing and which we improve upon being taught them. Kaplan describes the "mathematical knowledge" part as:
The Mathematics Knowledge section is a 24-minute, 25-question test of your understanding of a wide range of concepts in arithmetic, algebra, and geometry. You may still see the occasional word problem on the Mathematical Knowledge section of the ASVAB, but in general the questions, while drawn from a wider base of mathematical concepts, are more straightforward than the word problems found on the Arithmetic Reasoning section.
People can have lots of legitimate problems with various intelligence tests and how their results are interpreted without thinking they measure nothing.