There are a number of ways in which beat literature can be characterised as anti-intellectual. For starters, the beats generally valued spontaneity. Kerouac wrote a short essay called Essentials of Spontaneous Prose in which he urged writers to:
LAG IN PROCEDURE No pause to think of proper word but the infantile pileup of scatological buildup words till satisfaction is gained, which will turn out to be a great appending rhythm to a thought and be in accordance with Great Law of timing.
TIMING Nothing is muddy that runs in time and to laws of time-Shakespearian stress of dramatic need to speak now in own unalterable way or forever hold tongue-no revisions (except obvious rational mistakes, such as names or calculated insertions in act of not writing but inserting).
He wrote his best-known work On The Road in just three weeks on a single scroll of taped-together paper sheets, although he had previously prepared volumes of notes for the attempt and - against his own advice - made a number of revisions after.
Not all the beats tried to take these concepts so literally. Howl was inspired by a Peyote vision and Ginsberg took immediate notes, but he then worked on the poem in draft form over the course of several weeks, including revisions after he'd shown it to friends, although according to his own journals, he did try to find a "spontaneous" voice.
I labour the point of spontaneity because it is, broadly, the enemy of intellectualism. Vladimir Nabokov is on record as having slaved over short passages of Lolita for months, presumably to try and work in the various puns, allusions and symbolism that populate his work. It's hard to hide the rich seams of hidden meaning and cohesion that generally characterise "intellectualism" in literature without rigorous re-drafting and editing, which would seem to be the opposite of spontaneity. And while the reality of beat writing might not always have been spontaneous, it has that appearance about it and the authors seemed to value it, giving ammunition to their critics.
However, it isn't just the style of beat writing that appears anti-intellectual, but its subjects. The celebration of sexuality, drunkeness and drugs was a key concern of the beats, and giving in to one's animal impulses has long been seen as the opposite of a reserved, considered, and intellectual mode of life. Furthermore, their subjects were often the kind of "salt of the earth" characters who'd have no interest in intellectualism. Look at Dean from On the Road, a petty criminal who's more interested in pursuing "gurls" than dissecting modernist poetry, or the way the novel idolises farmers and hobos. While the real-life inspiration for Dean, Neal Cassidy, was a writer who certainly gained something of an intellectual bent, it's not hard to find genuine anti-intellectual sentiment among the social groups that beat writing celebrates.
You can see this taken further in Howl which actively encourages rebellion and criminality against what it sees as the far greater crimes of the capitalist system that it rails against. It's more of an active polemic than something Ginsberg wants critics to sit and pore over to tease out intellectual detail. Indeed, he seems pretty dismissive of the social classes most academics would see themselves as belonging to:
Holy the lone juggernaut! Holy the vast lamb of the middleclass! Holy the crazy shepherds of rebellion!
Another preoccupation of the beat writers was jazz and other emerging forms of popular music. While jazz, ironically, has gained a degree of intellectual credence over the years, it wasn't seen that way in the 50's. As one of the key critics of the beats, their contemporary Norman Podhoretz wrote:
To the extent that it [beat writing] has intellectual interests at all, they run to mystical doctrines, irrationalist philosophies, and left-wing Reichianism. The only art the new Bohemians have any use for is jazz, mainly of the cool variety. Their predilection for bop language is a way of demonstrating solidarity with the primitive vitality and spontaneity they find in jazz and of expressing contempt for coherent, rational discourse which, being a product of the mind, is in their view a form of death.
This neatly summarises the previous argument we made about spontaneity, while also bringing in their somewhat incoherent quest for an ill-defined spiritualism. It didn't matter to them that their apparent philosophical positions didn't bear close scrutiny: what they wanted was to portray the lived experience as accurately as possible, in all its chaotic glory.
Finally (we could go on but this is already too long for an SE answer, really) beat literature stood in opposition to the liberal politics that were emerging as an intellectual concern in the post-war world. In terms of social justice, beat writing veers from being disinterested at best to actively bigoted at worst. Women are often relegated to sex objects. Coloured people are envied as the source of jazz and their social struggles are ignored. Poverty and hunger are idolised, and the route out of them is capitalist consumption. This is a million miles away from the sort of politics popular in intellectual circles when the beats were rising in popularity and which remains popular today. As critic George Dardess put it:
On The Road is a love story, not a travelog (and certainly not a call to Revolution)
Whether these are fair criticisms or not remains a moot point. Certainly many critics and academics have found value in analyzing beat literature, if not anything like to the extent of their modernist forebears or postmodernist followers. Indeed it's interesting to speculate that, to some extent, postmodernism can be seen as an intellectual justification for their lack of a coherent project and their search for a language that effectively communicates the immediacy of life.
On the Holy Road: The Beat Movement as Spiritual Protest. Stephen Prothero.
The Harvard Theological Review, Vol. 84, No. 2 (Apr., 1991), pp. 205-222
The Know-Nothing Bohemians. Norman Podhoretz. Partisan Review, Volume 25, Number 2 (XXV; Spring 1958)
Dardess, George, 'The Delicate Dynamics of Friendship: A Reconsideration of Kerouac's On The Road, American Literature: A Journal of Literary History, Criticism and Bibliography, 46 (1974), 200-06