He was reluctantly so, but he explained his reasons circuitously and at length, here.
That link is from The Tank, which offered up these two paragraphs from Updike’s argument:
The protest, from my perspective, was in large part a snobbish dismissal of Johnson by the Eastern establishment; Cambridge professors and Manhattan lawyers and their guitar-strumming children thought they could run the country and the world better than this lugubrious bohunk from Texas. These privileged members of a privileged nation believed that their pleasant position could be maintained without anything visibly ugly happening in the world. They were full of aesthetic disdain for their own defenders, the business-suited hirelings drearily pondering geopolitics and its bloody necessities down in Washington. The protesters were spitting on the cops who were trying to keep their propertyâ€”the USA and its many amenitiesâ€”intact. A common report in this riotous era was of slum-dwellers throwing rocks and bottles at the firemen come to put out fires; the peace marchers, the upper-middle-class housewives pushing baby carriages along in candlelit processions, seemed to me to be behaving identically, without the excuse of being slum-dwellers.
Two other factors, it occurred to me at the time, inhibited me from taking the handy dove position. I had been to Russia, and I had not served in Korea, which had been my generation’s war to fight. I had hid out at Harvard, and then had not even gone into the peacetime army. I felt guilty at being 4-F, all the more guilty for being glad at the time, and hustling ahead with my career in those two years that I should have spent in barracks and canteens and the kind of boring clerical work that Philip Roth in his fiction has inflicted on Zuckerman. I would never know what I had missed, and read Roth’s fictional versions of his army tour with envious interest. If Roth in person said, as he did, that the generals and presidential advisers knew no more about Vietnam and its alleged strategic importance than we did, he had earned the privilege of dissent, it seemed to me, in a way I hadn’t. He had paid his dues. If Norman Mailer wanted to march in Washington and be briefly jailed and then write a funny, inflated, shrewd, skewed, pop-apocalyptic account of it, he, too, had earned the right, risking his life in the South Pacific against the fanatic Japanese while I, for my heroic part, was flattening tin cans in my grandfather’s chicken house. If Kurt Vonnegut, having survived capture by the Germans and the Allies’ firebombing of Dresden, wanted to fulminate in his woolly way against the powers that be, more power to him; he had paid a fair price for his skepticism and indignation. I had paid no such price; in fact, I had had a fine peaceful time being an American male in the middle of the 20th century. Defending the war (or, rather, disputing the attackers of it) was perhaps my odd way of serving, of showing loyalty to a country that had kept its hackneyed promisesâ€”life, liberty, pursuit of happinessâ€”to me.