Here is an interesting story on the Language Log blog about the impressions of a British Missionary in China in 1845 with respect to Chinese Muslims and their language.
On July 23, 1845, a British missionary named George Smith visited a mosque in the city of Ningbo, which is a major commercial city on the coast about a hundred miles south of Shanghai. He recorded the remarkable observations he made on that occasion in his book entitled A narrative of an exploratory visit to each of the consular cities of China (London: Seeley, Burnside, & Seeley; New York: Harper & Brothers, 1847), pp. 154-155:
The old (Muslim) priest was a native of Shantung [VHM: Shandong, a large province situated on the northeast coast of China; birthplace of Confucius and Mencius], having been sent for thence to Ningpo, forty years ago, according to the custom of supplying the priesthood, on a vacancy, from their original province. After we had taken some tea together, and made an exchange of some trifling presents, he sent his grandson to bring some Arabic books and portions of the Koran, which he appeared to read with great fluency. His knowledge of geographical names exceeded that of the generality of Chinese to be met with in the north of China. He mentioned the countries in which his religion prevailed, among which he named Bokhara, Madras, Turkey, and several places in Arabia. We adjourned into the temple, which was written over with sacred sentences from the Koran, and had a little ark for the sacred books, with a movable pulpit. I had previously supplied him and another Mohammedan with one of the gospels and epistles in Chinese, but was surprised to find, on asking the priest to read some Chinese inscriptions in the temple, that he was unable to decipher a single character, though he speaks the language very well, and has been during forty years a resident in Ningpo.
Later, as described on p.186 of the same book, Smith meets a Muslim shopkeeper, also a native of Shandong, who spoke Chinese but was “ignorant of the written character. The whole sect appear to devote their studies exclusively to their own sacred language, the Arabic. His bold features, prominent nose, and restless eye, confirmed the fact of the distinct origin of this descendant of Ishmael.”
From the evidence supplied by Smith, we learn that Muslim citizens of the late Qing / Manchu period (the last dynasty [1644-1912]), who were fluent in one or another of the Sinitic languages, were illiterate in Chinese characters but literate in Perso-Arabic script. This information is all the more stunning in light of the fact that Muslims in China developed a system of writing Sinitic languages (primarily one or another topolect of Mandarin [especially in the northwest], so far as I know), in Perso-Arabic script. This was called XIAOERJIN or XIAOERJING. Although the etymology of XIAOERJIN(G) remains uncertain, this Perso-Arabicization of Sinitic was important in the spread of Islam in China.
The above information would seem to indicate that it was much easier to become Sinitically literate in Perso-Arabic script than in Chinese characters. This conclusion (that it is easier to become literate in an alphabetic script than in a morphosyllabic script) is supported by the fact that tens of thousand of Sinographically illiterate Dungans who fled from persecution in northwest China during the late 19th century acquired literacy in their own northwest Mandarin topolects first through the Perso-Arabic alphabet, then through the Latin alphabet (1928-1953), and since 1953 through the Cyrillic script.