Here is a comparison of original "Raghupati Raghava" song from Nama Ramayana and Gandhi's distortion of it. Gandhi tampered with the famous Hindu prayer to suit his political interests. Tampered version which includes "Allah, Rahim" has been popularized by Indian secularists. 
Gandhi tampered with Hindu prayers to include "Allah, Rahim, Karim" and became a "Mahatma" for it. But even Gandhi knew what would have happened to him had he tampered with Islamic prayers/Shahada to include "Jai Varaha".He never touched them Indian secularism is one way street
A very important point. Gandhi NEVER worshiped the Hindu deity Rama. As Gandhi himself made it very clear in his Ramanavami speech, Gandhi's Rama is not the Rama of Hindu scriptures. Gandhi's "Rama" is a monotheist formless God. Excerpt from Gandhi's Sabarmati speech,1928
To drive the point home, Gandhi even revealed that according to him, the Hindu God Rama of Hindu scriptures was not the "perfect one". The Hindu God Rama was just a "monster" Peace would not be attained through him. It would be attained only by worshiping monotheist formless one
So,the "Rama" of Gandhi was not the Hindu deity Rama. He was just a monotheist formless God who was also known by other names such as Allah, Rahim, Karim. Keeping this in mind, let us take a look at the lines which Gandhi pruned from the original "Raghupati Raghava" bhajan.
Gandhi removed the line "सुंदर विग्रह मेघश्याम" clearly because physical description of Hindu God Rama as मेघश्याम did not go well with his monotheist formless God. Replaced it with "ईश्वर अल्लाह तेरो नाम" so as to clarify that his Rama had nothing to do with Hindu deity Rama
Gandhi removed Hindu references from the song so as to make his God as close as possible to monotheistic formless Abrahamic God. He simply tried to Abrahamize an ancient song. If that can be called inclusive, placing idols in Babri Masjid should also be called "inclusive"
