The pattern of interaction of two competing memes always interesting to observe and it follows the similar pathway of Darwinian Natural Selection. Here is the account of the patter of interaction between Indic and Abrahmic religious and civilizational memes in India from my perspective.
It is competition between two memes competing for more followers. Just like Buddhism and Astika schools were in competition with each other in post-Mauryan India, Abrahmics and Indics are in competition in India for similar goals.
Both astika schools and Buddhism/Jainism were Indic traditions and followers of same civilizational scaffold. Hence, all the differences amongst them were solved in debates and not on battle-grounds. Furthermore, both parties were equally agnostic and free-rationalists. Agnosticism makes person humble and enables him to entertain a rival thought in his mind, even if he does not accept it.
The Abrahmic religions belong to region outside the domain of Bhaaratiya civilization. Their values are different and they are extremely intolerent about rival ideas. They are extremely sure about the truth of what they believe in.
Indics are never completely sure about their convictions. They are open to amendments because they acknowledge that what they stand for may not be absolute truth and this thought does not make them uncomfortable. Abrahmics are total opposite to this. Hence, they have an inherent sense of their superiority over other people who are not fanatically sure about what they believe in. These people are referred to infidels/Kaafirs/heathens etc. Every Abrahmic religion prophecises complete moral, political and social superiority over the non-believers and approves, rather does not disapprove, any action to undermine the influence of other non-self memes.
Indics have segregated faith and sociology, yet both are beautifully interwoven to form the fabric of Bhaarat. It is like weaving a cloth out of different threads which are of different colour and identity. Although the cloth seems contiguous, it is made up of threads which are on fundamental level separated from each other. Faith and social order in Bhaaratiya system is like this. Faith in Bhaarat, although seen everywhere in society, is peculiarly a personal trait. The Dharma of an individual is constant and independent, irrespective of what faith he adheres to. A king may be a buddhist or a Shaiva in faith, his dharma as king is constant and is not at all influenced by what faith he follows in personal life.
Abrahmics (Islam in particular) cannot segregate Dharma from Faith because there is no concept of Dharma in first place. Hence, faith governs everything. And their faith is such that it inculcates in mind of follower that if he is following the book he is always right, without exception.
Indic memes cannot defeat such arrogant abrahmic memes with their trade-mark scepticism. Yes, this ensured the survival of Indic memes in turbulent times. This scepticism and multiplicity coupled with decentralized varna system ensured that Indian civilization did not suffer the fate of Zoroastrian Persia. But, Indic memes could not pay back the Abrahmic memes in their currency except during Battle of Rajasthan. And unless Indic memes do not pay Abrahmic memes back in their own currency, the problems will persist in Bhaarat.
This is because, Indic memes cannot suffer the presence of foreign cultural and civilizational influence in Indian subcontinent. Again this is the trait of our civilization, which has its roots in Varna system. Foreign memes are considered impure at the best and barbaric at the worst by Indic memes in general and Orthodox Astika memes in particular.
The sense of superiority is required to remove the doubts in minds of an Indic while dealing with defeated enemy. Instead of behaving like Sri Raam, Indic victors have behaved like Arjun in self doubt, while dealing with defeated Muslim enemies (example Prithviraj Chauhan, Marathas). Sri Raam on defeating raakshas people was benovalent with them after overwhelming them completely. He kept Vibhishan under his check, awe and influence to such an extent that Vibhishan became the devotee of Raam and adopted Raam's style of life. Arjun OTOH was in complete doubts on the eve of battle regarding his behaviour with his enemies.
This doubt at wrong places encourages the feeling of "enmity" within the enemies. Indic victors encouraged the enmity by not crushing it completely and thoroughly. This arose out of lack of sense of overwhelming superiority over vanquished Islamic foes in minds of Indics and Abrahmics. Even the vanquished should feel that the victor is superior to them in all aspects of life and that becoming like him is the best thing in the world. Enmity cannot be defeated by defeating the enemy. Enmity is only eradicated by making the propagation of enmical ideas non-sustainable for propagation and survival. Enmity should not provide any selective advantage to the group of people harboring it in their minds.
This eradication of enmity has been the traditional response of Bhaaratiya civilization towards invading foreign civilizations. Indian civilization did this with its every other foe, except Abrahmics. And to defeat them, this is what needs to be done.