Hey! I see this question has gotten quite a bit of attention and I'm going to ruin everyone's day by answering... No, I have never read or heard of any instance where rural Chinese populations believed that after 50+ years of civil war, internal strife, and Japanese invasion, that the Qing were still believed to be in charge. This claim almost certainly comes from the idea of rural backwardness in developing countries.

Going in depth, if you lived in rural China from 1926-1949, you were almost certain to have your fair share of run-ins with CCP officials before even meeting a KMT official, and especially one that wasn't just a tax collector. By 1927 the CCP had shifted much of its ideology. After the disastrous Autumn Harvest Uprising and the communist attempt to seize Nanchang and other large Central China cities, Qu Qiubai was kicked off of the presiding board of the CCP in 1928. Mao, on the other hand, became increasingly power due to his focus on rural Chinese peasantry and rural guerrilla tactics. Although it would still be another 10 years or so until Mao's dominance over the CCP came to fruition, another string of heavy defeats of the CCP under the leadership of Li Lishan, and then the "28 Bolsheviks" led by Wang Ming led many communists to believe that focusing on Russian-style urban revolution was useless in China.

Thus, upon Mao and Zhu De's establishment of the Jiangxi Soviet in November 1931, most CCP agents shifted focus to the rural peasantry, who is seen in Maoism as the core revolutionary element to achieving Communism. If you know anything about Marxist ideology, you realize that this is a total 180 degree shift in leftist ideology. And indeed it was. But whats important for the question here is that the CCP spent decades establishing a base of support and loyalty among rural peasants, especially those in the North-Northeastern part of China, which is also the part of China hit heaviest by the Cultural Revolution and Red Guard units. Throughout the Sino-Japanese War, the communists relied heavily on rural recruitment to fight Japanese occupation.

Now let's fast forward to the 1940-60s. The CCP has defeated the KMT and is ruling over mainland China, and things for both rural peasants and urban workers are gonna change. fast. In rural areas, Mao instituted programs of land redistribution among peasants in 1950-53. The rural population was given a special role in Mao's China; they were to become the agricultural behemoths which would feed the rapid industrialization and urbanization of China into a proper communist state. Or at least that was the theory. Still inbetween 1950 and 53 over 700 million mu of land (1 mu = .0667 hectares) had been confiscated and redistributed by the CCP. This was distributed to over 300 million peasants, or the vast majority of the Chinese population in 1953 (which would've been at about 450-500m). Furthermore, these farmers were organized into People's Communes, led by Communist agents. Technically, all heads of villages in rural China were Communist Officials, though how loyal they were to the Party higher-ups is a matter of debate, especially after the Great Leap Forward's disastrous outcome.

Anyway, let's fast forward to the Cultural Revolution in the 1960-70s like your question is relevant to. Like I said, there may have been some area of China that everyone (or at least I) overlooked, but this is highly unlikely. When "counter-revolutionaries" were sent into exile, we're talking about the most isolated, deepest rural parts of areas like North-Northeastern China in Heilongjiang for example. These farmers would've had a hunch as to why they're suddenly getting a bunch of urban intellectuals from Beijing coming into Nowhere, China. Even some of the most in-depth studies of rural China, I'm thinking particularly Revolution, Reform and Resistance in Village China by Edward Friedman (2007) highlights the political struggle between rural party leaders, their peasantry, and then Red Guard leaders and their followers into rural Northeastern China.

In the end, by 1960 everyone in China knew who the communists were, and especially they were well integrated into Mao's cult of personality. I have never heard of the claim that there were isolated villages that believed the Qing were still out there running things, and I suspect this is some sort of hogwash that popped up a while back stemming from god knows what. But one of the core elements of not just Maoism, but in general all Marxist-Leninst derived ideologies is a strong central state that plays a vital role in both urban and rural politics. Professional revolution, led by professional revolutionaries that organize society on a massive scale. This had been done in rural China among the peasantry for decades prior to the CCP's victory in 1949, and would continue far after 1949.

Sources:

Chinese Village, Socialist State, Edward Friedman

Revolution, Resistance, and Reform in Village China, Edward Friedman

A Nation-State by Design: Dynamics of Modern Chinese Nationalism, Suisheng Zhao