I'll try to answer you question, sorry if it doesn't satisfy you. However, i think the question is too broad so i'll divide it into countries/regions and focus mostly on Muslim intellectuals and journalists on Palestine, India, Egypt, and Dutch East Indies. There are also responses from places like Albania, Morocco, and Bosnia but i'm going to focus on those four.

Palestine

Palestinian Arabic press generally denounced the abolition. The newspaper Al-Karmil contained an article titled "A Dangerous Step in Ankara". In it, the author Yusuf al-Khatib attributed the Kemalist abolition as an act of hubris. He stated:

It seems that the brilliant victories of the Kemalists, which all nations of the East have applauded, have tempted the people in Ankara into thinking that they are capable of fulfilling all their desires, and so they have publicly announced the implementation of a new regime in the Islamic Caliphate and in Turkey

He was at loss at the decisions made by the Grand Assembly, he pointed out that as the Sultan had already recognized the Assembly and the government in Ankara, Mustafa Kemal could just become the grand vizier and made his word count in the Grand Assembly. The author claimed (or deduced) that the reason Atatürk abolished the Sultanate was pure arrogance and ambition: "Notwithstanding our respect for him, we believe that he yearns after the presidency of a republic, as we can infer from his glorious personal history crowned with a love of pomp." On the impact of the abolition of the Caliphate, Yusuf al-Khatib stated that stripping the Caliph of its authority was not a good move for Turks or Muslims in general. For this he cited the story of the Abbasid Caliphs, who had been stripped of political authority and reduced as puppets at the hands of the Sultan, and argued that the Ottoman Sultanate owed its existence to the Ottoman Caliphs’ exercise of both spiritual and temporal/political power. He further added that "Separating these two powers now will therefore inflict harm on the Turkish State" and that "One of the most important causes of their (the Kemalists) victories and moral strength, had stemmed from the Muslims’ desire to see full authority restored to the Caliph." Additionally, he further observed that the abolition would also prove detrimental for the nations of the East who had regarded Turkey as "A mature brother and a powerful and resilient leader". Further articles in Al-Karmil also further revealed it authors' thoughts on the abolition. Yusuf al-Khatib on his another article "The Caliphate and the Islamic World" had also attributed the abolition to the influence of Communism. he stated the reason why the peoples of the East had taken a close interest in Turkey’s victories was that the reestablishment of the Caliphate would form a "‘powerful barrier that would prevent Communism from afflicting the East – disinclined as it was to accept that ideology and adapt it according to its own mentalities and traditions." To add to this, Najib Nasser, the editor of the newspaper later published an article "The Abolition of the Caliphate and its Reasons". In it, he addressed the abolitions of the Greek Patriarchate and the Jewish Rabbinate in Turkey:

This demonstrates the existence of an anti-religious movement stirred up by its originators against religion, or to be exact, against religious authorities. If this argument is correct, then the East is heading towards a religious and social revolution whose origin is Russia

Filastin, another popular and well-regarded Arabic newspaper also stated their opinion on the matter. Filastin take an anti-Semitic turn and squarely blamed the abolition of the Caliphate thanks to the influence of Russian Jews and the Dönme, descendants of the converted followers of Sabbatai Zvi in Turkey. In an article titled "The Abolition of the Caliphate in Turkey: In Every Valley there are the Tracks of a She-Fox" the editor Isa al-Isa claimed on the basis of Protocols of the Elders of Zion that the ‘conspicuous factor’ in all the revolutions from the French Revolution to the Ottoman Revolution of 1908, and even to the revolutions in Germany had been the socialist ideology, whose originators were none other than the Jews. He argued that the Socialist Jews, by destroying the monarchy and the aristocracy and separating religion from politics could deliver the reins of all the world’s governments to Jewish capitalists. He asserted that "the abolition of the Islamic Caliphate and the deposition of Abdulmecid today, as well as the sentencing of the Caliph and his family to departure from Istanbul, are all the doings of the Jews and of that sect known as the Dönme." On the effects of the abolitions, Isa al-Isa stated:

The affair of the abolition of the Caliphate and the deposition of the Caliph has had a seriously negative effect on the minds of Muslims in general. They have grown indignant against this deed of the Turks, and some of them have regarded it as an assault on religion. The echo of this indignation still reverberates in the East and the West

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