The association doesn't have to do with "real" surfing culture other than a relatively universal preference in the US for pizza, and the word "pizza" doesn't appear at all in The Encyclopedia of Surfing, makes no cameo in the documentary The Endless Summer, shows up nowhere in The Pump House Gang (the Wolfe book about 60s surfer culture), and only appears once in The American Surfer: Radical Culture and Capitalism (and in reference to a movie I will be discussing). Pizza was a perennial "all ages" food all the way through the Cold War, and the 60s and 70s reinforced this with an explosion of "pizza-and-pipes" establishments where organists would play to accompany pizza eaters (the trend was started by Ye Old Pizza Joint in California which had a 1928 Wurlitzer); this was later developed by Nolan Bushnell with the animatronics of Chuck E. Cheese (where he admits his idea for the format came from the pizza-and-pipes places).
In fact, the association is mostly with Teenage Mutant Ninja Turtles, but it was arguably totally by accident due to a a completely different book/movie and a change in how a certain real-life story was conveyed.
For seven years I wrote articles for a youth culture magazine, and perhaps not a day went by when this term wasn't used -- "the kids" ... Kids were discussed as if they were some enormous whale, to be harpooned and brought to shore.
-- Cameron Crowe
In the fall of 1979, at the age of 22, a young and precocious Cameron Crowe -- having already graduated high school 7 years before -- approached Principal William Gray, of the very real Ridgemont High situated in the beach area of Southern California. (While the characters and places are real, all names are changed for journalist protection.)
His proposition was to go undercover. He would pretend to be a high school student for the term in order to write a book about "real, contemporary life in high school."
Mr. Crowe at this point was already a fairly prominent writer, and in fact had been a contributor to Rolling Stone for 7 tears. He rattled off rock stars who he had profiled, including Kris Kristofferson, and Principal Grey agreed to the idea.
I was never found suspicious. In fact, for the first month, I was completely ignored at Ridgemont. I eavesdropped on conversations around me, made copious notes, winked at the teachers who knew, and made my way.
After his undercover stint was over, he interviewed his "main characters" in order to get more details, and wrote a book on the year, noting that
The only time these students acted like kids was when they were around adults.
The book, Fast Times at Ridgemont High, was turned into a movie. The relevant scene for our question is from a chapter called The Attitude, and refers to a students named Mike Damone and Mark Ratner ("The Rat"), both "cool" students who have The Attitude (as Damone says, "When you are the coolest and the cruelest, then you have The Attitude.")
As an illustration of The Attitude, several weeks into the term, during fourth-period biology, Damone asked the Rat if he was hungry.
"Wouldn't you love a pizza right now?"
"Don't torture me."
A few minutes later, there was a knock at the front door of the classroom. Mr. Vargas had been giving a lecture. HE paused to answer the door.
"Who ordered the pizza?" asked an impatient delivery man for Mr. Pizza.
Damone waved his hand. "We did back here."
The book was transformed (script written by Crowe himself) a year later into a movie, where the person ordering the pizza is the surfer Jeff Spicoli (as played by Sean Penn) and Mr. Vargas becomes Mr. Hand. (Video clip here.)
Pizza delivery person: Who ordered the double cheese with sausage?
Spicoli: Right here, dude.
This was one of the most famous scenes in the movie, and did make media association surfer-slackers with pizza, even if the cultural links in real life weren't ever particularly strong. It was iconic enough to influence the major thing the question seems to be referring to, the Teenage Mutant Ninja Turtles.
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The comics, by Kevin Eastman and Peter Laird, were originally made as a parody joke. Eastman had drawn a turtle standing with nunchucks, and Laird made his own version. Eastman followed by making an entire set of four turtles putting the titled "Ninja Turtles", and Laird added the "Teenage Mutant" part to the title.
The turtles eventually got names after Renaissance artists, aided by a copy of Janson's History of Art, although Michelangelo was originally spelled Michaelangelo.
This ended up being the source of what was to be a "one-shot" comic by Mirage Studios (named that because of the actual lack of studio -- it was just Eastman and Laird) where the duo managed to scrabble together enough money to print copies and put an ad in Comic Buyer's Guide Magazine, a publication intended for comics distributors.
The run of 3000 sold out quickly, leading to another run of 6000 which also sold out; things went well enough that an issue 2 followed in 1985, eventually getting to 135,000 copies sold by issue 8.
The skew was definitely for an older audience -- not R rated, exactly, but there was some cursing, and rather than an affinity for pizza, the turtles had an affinity for beer.
The turtles were eventually picked up for the mainstream (with Mark Freedman getting rights and enlisting help from Tony Marsiglia, president of Responsive Marketing Communications, Inc.) and a cartoon series started in the late 80s. This is when changes were made, and the pizza obsession began. Quoting Laird, discussing if he approved of the changes and what he would have done differently:
Among other things, there would likely have been no moronic henchmen like Bebop and Rocksteady. The Shredder would have been seriously malevolent. April would not have been a reporter and constantly need to be rescued by the Turtles. The Turtles would not have been so ridiculously obsessed with pizza, and the Shredder would not have had as one of his businesses a restaurant called ‘Ninja Pizza’.
While it is clear why the switch from beer happened (given the age demographic was now shifted to single digits), why the switch to pizza? There is a story about Eastman and Laird commonly eating pizza while working on the comic, but this seems to be not be the real story (especially given Laird's disapproval). The surfer-dude conversation was already there (witness these panels of drinking beer) and pizza was both child friendly and held some recent media association due to Fast Times. (And, let it said, able to be marketed -- there were roughly 200 companies involved during Turtle-Mania of the early 90s, with one item being "turtle-shaped frozen pizza".)
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I did hint earlier about a change in a certain real-life story. If you remember, the person who ordered the pizza in the movie was the surfer-dude. This was somewhat thematically appropriate for rebellion (and as Radical Culture and Capitalism notes, critique Mr. Hand's idea of "my time" being wasted) but the real person behind the pizza-ordering stunt was none other than "The Rat", Mark Ratner (real name Andy Rathbone), who would later go on to fame and fortune for his book Windows For Dummies, a New York Times bestseller and one of the very first of a long-running series which now has nearly 2000 different volumes.
So if Spicoli's "right here, dude" contributed to Freedman's (and the marketers') use of pizza, the rad association with pizza really might have been an accident due to real events being tweaked for dramatic purposes.
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Crowe, C. (1981). Fast Times at Ridgemont High: A True Story. United States: Simon and Schuster.
Farago, A. (2014). Teenage Mutant Ninja Turtles: The Ultimate Visual History. United Kingdom: Insight Comics.
Jorgensen, J. (ed.) (1994). Encyclopedia of Consumer Brands: Durable goods. United States: St. James Press.
Lawler, K. (2010). The American Surfer: Radical Culture and Capitalism. Taylor & Francis.
Thorson, E., Moore, J. (ed.) (2013). Integrated Communication: Synergy of Persuasive Voices. United States: Taylor & Francis.
Warshaw, M. (2005). The Encyclopedia of Surfing. United States: Harcourt.