Do you want to know the effects of the Mughal Empire on Buddhism, or Islam in general ??? I think you asked the wrong question LOL Your question should be what was the effect of Islam on Bharati Buddhism, well as someone mentioned it in the other thread already, buddhism was almost non existant in INDIA(speaking of present day India) at this time,except some parts of Indian Kashmir,most of its people were Hindus.If you'd have asked us, what the effects on Bharati Buddhism were.I'd tell you that in the region of present days Pakistan, before the advent of Islam, the majority of the people living their (Indus Valley region) practised mostly Buddhism and in lesser degree Animism,Paganism,Shamanism and Zoroastrianism.So When the Muslims invaded Pakistan, the majority of its people were Buddhists.You can see it even today, the word for idol in Urdu(the official language of Pakistan) is "budh",and idol worshippers are called "budhparast",very ignorant

afterall only some buddhist sects worship Buddha(PBUH),Buddha(PBUH) himself told people not to worship him(sounds similar LOL).I don't think that Islam effected Buddhism in its philosophy/practise, the effect was more that these buddhists converted to Islam,I should say reverted LOL there is no thing as converting to Islam...They reverted not because of the Mughals, but because of Sufism(Islamic Mysticism),The Islamic influence in this region began a long time before the Mughal Empire.Islam was introduced there ca. in the 1st century after the death of the Prophet(PBUH).
btw Mahayana Buddhism originated in Pakistan

Well if you want to know more about the interaction between the buddhists and muslims before the Mongol Empire,just tell me LOL i'll provide you some links.