One of my favourite examples to demonstrate why Hindus and Muslims are like chalk and cheese (or cheese and chalk- no value judgment implied by the metaphor!) is their respective treatment of Jains and Ahmadiyyas.
We all know about the plight of Ahmadiyyas in Pakistan. Not a week goes by when there isn’t a story in the media on Ahmadiyya persecution. To Indian eyes, this can be quite baffling. The Ahmadiyyas reserve a highly exalted position for Prophet Muhammad. By all socio-cultural markers: naming and dressing conventions, eating habits, praying patterns etc., they appear “Muslim”. Yet certain theological red lines are crossed- including the recognition of Indic icons such as Buddha and Krishna as prophets, but most importantly the perceived violation of the doctrine of Khatam-un-Nabiyeen: the finality of Muhammad’s prophethood. A clear case of orthodoxy trumping orthopraxy. This hostility towards the Ahmadiyyas is not a recent phenomenon and can be traced back to the views of the founding fathers of Pakistan, such as Allama Iqbal.
From a Hindu perspective, this can appear bizarre- ethnic Punjabi “Muslims” who share so much in common in both cultural and kinship terms are so hostile towards each other due to some theological disputes. There are more consequential theological disputes within sects of Hinduism. For example, within Vaishnavism, there is the Dvaita Vedanta school founded by the 13th century scholar-saint Madhavacharya which believes that the Divine (i.e. Vishnu or the supreme being) is distinct from the individual. The better known Advaita Vedanta school founded by Adi Shankaracharya is Monistic (i.e. believes in the essential unity of the Divine or Vishnu and the individual). From a theological perspective, these ruptures are perhaps as radical as those between Sunni Muslims and Ahmadiyyas. Yet, the average modern Hindu, even someone who self-identifies strongly as a Vaishnavite, would find the notion of being hostile to other Vaishnavites on the basis of doctrinal differences to be bizarre and laughable.