IMHO, the 'first cause' of this religion things in Indonesia is in the taken for granted, unchangeable, undebatable: Pancasila itself, the dasar negara/ideology of the state. It's the number one, sila pertama: Ketuhanan yang Maha Esa/Believe in One Supreme God.
So, the state ideology has started the discrimination right here. It implies that Indonesia is a state whose peoples believe in One Supreme God. They can not be atheist nor doubt the existence of God, like agnostic, nor believe in many Gods or Godesses (although there's no God in budhism, AFAIK, the state consider their adherents as Pancasilaist and categorized budha as one of the official religions).
The state itself has no religion, and can not have religion, because the state is not a human being.
It would be very difficult to change the Pancasila, but probably we could interpret it as: Indonesian has somewhat spirituality, they are not puritan materialistic. Sort of. But this is not the state, the government, nor the parliament did and does all this time. In the future, I don't know.
Evenmore, I'm not sure exactly where the state puts it, in what kind of regulation, surely not in our constitution, but there're some official religions in Indonesia: islam, protestant, catholic, hindu, budha, and Gus Dur adds one more: kong hu cu/confusianism. Honestly, I never know what 'official' means here. That each religion has national holidays? Or those religions have office in the government bureaucracy, in Ministry of Religion, while the rest of religion such as kejawen, kaharingan, etc will be considered as 'culture' and their office is in Ministry of Cultural Affairs and Tourism.
Frankly I don't know how government decided which one is religion and which one is culture, apart from the statistic of its national or international adherents. For all I know, letting state or government makes decision about religion is dangerous. Peoples will look at government to ban Ahmadiyah, which is considered as for instance.
Further, there's a ministry of religion. What's this ministry does? Dealing with haj pilgrims transportation and facility in Mekah and Madinah? Puuhlleesss….
So, before we could erase religion part in KTP, three things we need to do–as Indonesian. First, change Pancasila, or at least make new interpretation of Pancasila acceptable. Second, wipe out 'official' religions category, just make important religious day as national holiday base on statistic; and lastly, dissolve (bubarkan) Ministry of Religion.
But to start this, Indonesian peoples have to change their view about religion, they have to make it personal affair and not state affair. They have to change their attitude too so they are not so nosy about someone else's religion or irreligiousness.
Where to start? Better education? Sure. Better law and law eforcement? Impartial justice system? Sure. Better public service, such as free healthcare? Better economy? There's some influence, of course. I mean, in a bad economy situation, when the gap between the riches and poors is so wide, peoples would be easily blame other peoples with 'wrong' ethnic, or religion, that's why many peoples still needs religion column in KTP. Some candidates who ran for presidency or parliament seat also played this religion-ethnic card in their campaign, and they'll keep this card to preserve support. This also adds to why we still have the religion column in KTP.
It will take a very very long overhaul.
I guess.