The reality is, of course, that their kids weren't nearly as conservative as the parents thought. But that doesn't stop the salient myth of liberal indoctrination in colleges.
Trade schools come into play mainly as a totem to hold up against liberal colleges. They are being played up as a sort of bastion of conservative thought, mainly because they don't have those pesky general ed requirements that might accidentally tell people how to fight against the elites running the system.
There's a kernel of truth in all of this, in that there's some trades that shouldn't have been left out of the STEM paths that colleges like to push as an obvious moneymaker. The culture war is ultimately one of mottes and baileys, where you take some truth and ride it as one's political hobby-horse. Hell, just to explain why this happens I've already had to do the same thing.
[0] In the same way that some people think tech companies can "hack our dopamine loops" or whatever