Okay, before I dive into the resistance that took place during the Cultural Revolution (and there was a fair bit), I want to put the Cultural Revolution into context. The Cultural Revolution was not just one monolithic 'movement.' It was the physical manifestation of a fierce political struggle between moderates, consisting of prominent CCP officials such as Liu Shaoqi, Lin Biao and Deng Xiaoping on one side, and CCP traditionalists such as Jiang Qing ("Madame Mao"), Yao Wenyuan, and the rest of the Gang of Four. Other prominent officials such as Zhou Enlai (who is generally considered a moderate) would act pragmatically, able to keep their positions throughout the chaotic purges that ensued. These political tensions are seen to have arisen primarily due to the Sino-Soviet split, and the proposed detente by Henry Kissinger and potential future cooperation with the US. Some more conservative elements of the CCP saw such events as China betraying its revolutionary fervor, and selling out Maoism. As for Mao himself, he bounced around considerably, and enjoyed the protection his new cult of personality provided. Read the following quote, and consider the mindset many young Chinese went into the Cultural Revolution with:

China's youth, long alienated from the privileged party apparatus, their aspirations stifled by reduced educational opportunities in the wake of the Great Leap economic decline, and their critical faculties sharpened during the socialist education movement and the four cleanups, joined Mao's crusade against false socialists. When children played out the battles of the Three Kingdoms era, they said that Zhuge Liang, the brilliant strategist, was like Premier Zhou, but no one was said to be comparable to Mao. He was god-like. Young people wanted to prove themselves worthy of Mao and superior to the party people in power who had betrayed Mao, mocked the young, and blocked their rise. - Revolution, Resistance and Reform in Village China, 85.

Now, onto your question. The book I'm going to be using to help explain the chaotic violence of the Great Proletarian Cultural Revolution is Revolution, Resistance, and Reform in Village China. This classic work, which took a quarter of a century to compile, was finished by the three now-famous Sinologists Mark Seldon (a historian & sociologist), Paul Pickowicz (a historian), and Edward Friedman (a political scientist). The three made more than 30 trips to the little village of Wugong (Raoyang county of Hebei) in the 1970s. Although small, the village's proximity to Beijing (120 miles away) made it the target of urban Red Guards who would often come down and harass local CCP cadre, so I think this is the closest relevant book to your question. It also covers some of the violence that happened in Tianjin between Red Guard 'groups.'

In the big city of Tianjin, different Red Guard factions would often fight each other. The August First Group and the Defender of Dong both attacked each other at Nankai University (in Tianjin). According to the book, each day dozens of new dead would lay on the streets of Tianjin. These violent urban battlegrounds were much more deadly than rural environments. Stories of students hanging high school principles and teachers circulated, with Red Guards forcing the teachers left alive to kiss the dead corpses of their colleagues. These are awful times to be Chinese, regardless of where you stood. Page 87 states:

The most violent group, August 25th, came from the Tianjin Academy of Engineering, although some thought Nankai's August 13th even more brutal. The factions at the academy welcomed factory workers to join the struggle... The 66th Army was unable to maintain order. Blood had to be repaid in blood. Hundreds died in continuous fighting by both high school and college students. After public degradation and torture, suicide proliferated. They seemed more numerous than murder. The military wavered, its ranks divided, uncertain whom to support, whom to suppress.

As you can see, this type of activity muddles your question a bit. Who exactly was a 'targeted population'? Regardless, in the urban environment things were bloody.

Now, what goes on in Wugong, the little village, is somewhat of small-scale of what happens in Tianjin. The events going down in Tianjin inspired the students of Raoyang High School to organize their own Red Guard. A recent famine and earthquake in and near Wugong exacerbated the already desperate situation for the villagers, and when Red Guards came down from Tianjin and Beijing linking with local Red Guards, they set to work ridding the rural village of many of its traditional customs, such as weddings, dowry, and religion (by burning books and destroying icons of the Buddha). Begging, which many villagers had to resort to, was also illegal. The two groups, rural and urban Red Guards, would detain local leaders who were labeled as 'revisionists.' In reaction to these attacks on officials and literati, local leaders would attempt to organize their own groups which would show their profuse loyalty to Mao. In this case, Geng Changsuo, the former 'Boss' of Wugong village, urged those under attack in Raoyang and Beijing to unite, but there was not much they could do after Mao lifted travel bans in 1967, allowing Red Guards to link up with one another, going from village to village, destroying. Still, the Wugong locals would fight back whenever they could. When the Red Guard went after Geng Changsuo himself, and after a lengthy interrogation about Geng's past visit to the Soviet Union in 1952, violence broke out:

Villagers pushed their way into team 3 (Red Guard) headquarters as word of the confrontation spread. There was shoving; punches were thrown. An old man shouted at outsider Li Changjin "Our old coop leader (Geng) is a revolutionary. What the hell are you?"

The next day, a poster charged Geng with "stirring up the masses to attack the students!" A Geng loyalist countered by tacking up a cartoon portraying outsider Li Changjin with a huge nose trying to "smell revisionism" in Wugong. Nankai Li cursed the whole village, "These motherfuckers are hard to deal with!" One of the cooks, overhearing Li's remark, shouted back, "Who do you motherfuckers think you're talking about?" - pg. 104-105.

Geng, the old boss of Wugong, had the loyalty of many of the villagers, who resented the Red Guards, but not all village bosses were so lucky. This is just one theater of the awful violence that took place throughout China during the Cultural Revolution. So in conclusion, there were attempts at organizing resistance against Red Guards in rural areas, but they were rarely (if at all) armed. Nor were they as organized and powerful as the Red Guards, many of which saw materiel support from local PLA units who would give them AK-47s, bayonets, and knives to attack 'revisionists.'