Completely agree. I am a realist and believe Islam cannot be disassoicated with Pakistani identity. However it is not the only thing that defines us and realizing that is important. I always see Pakistan as a country very similar to Spain. Multicultural, multi-linguistic nation, born out of religious strife and for its initial period using religion as the sole identity marker, before Spanish identity became strong enough to gradually coexist with Catholicism (and for many Spaniards completely replace). Heck, even the first Spanish monarchs were referred to as the "los reyes catolicos" (the Catholic monarchs). Ultimately a shared history, folktales, geography and increasingly even cuisine are also large identity markers which will gradually shape Pakistani identity. The onus is on the state to reinforce this identity, rather than relying solely on religion. This will reduce Pakistani inferiority complexes viz a viz Middle Eastern/Arab Muslims and increase self-respect.
As for the "not India" part, all neighbors around the globe have things in common. However because India is so huge it is bizzare for us when we are said to be the "same" as a Tamil or an Assamese. Since India is much more than an Indian Punjabi or an Indian Kashmiri this is why the "Not India" mindset is prevalent amongst Pakistanis.