Anti-intellectualism can be described as a distrust of the academy, the traditional source of the intellectual, and the things that symbolize it.
Certain words, sentence structures, writing formats, dress codes, mediums for those words (audio, video, internet, print), gestures of approval, etc represent the intellectual institution and others represent those excluded from the institution, and anti-intellectualism is the ranking of these presentations.
Since anarchist efforts don't originate in academic institution, anti-intellectualism does not need to have an adverse effect on them. Often it can support a critique of the academy and the specialization and privitization of ideas, which coincides with anarchist perspectives. It might sometimes be a way of opening up the ways we can think about things, or what it means to be smart.
That said, anti-intellectualism can be conflated with being anti-theory, anti-reading, anti-writing. It can encourage a climate where people don't know how to critically engage with material, media, or each other. It also can be a way to reinforce the dichotomy between using our brains and using our bodies. That is a sad dichotomy.
*edited to be more wishy-washy*