It wouldn't seem sensible to, upon seeing religion-based conflict, just get rid of religious schools. I don't think it's the answer as it's not solving the problem.
It would be much more effective, to (somehow) change people's approach to different religions, by exposing them to them. This would definitely raise tolerance levels towards different groups of people and in turn could reduce conflict. It's easier said than done, but in an ideal world...
On the other hand - with schools being the main place where kids interact with other kids - do religious schools segregate children of one religion from those of another? If all schools were mixed-religion or "neutral", children would end up being passively exposed to a much wider variety of religions. For that reason, schools that are not religion-specific might be the ones that raise a generation more tolerant of different religious backgrounds, because after all, interaction is the first step to understanding.
I definitely don't think the subject of religion should be avoided in schools; this would be likely to create even more tension. If kids are exposed to kids from other religious backgrounds, society will start to get more and more cohesive and mutual understanding will start to rise.
I stand by the fact that people should be allowed to practise the religions they want, whether that be just in personal life or through school life too. Religious involvement shouldn't be limited by making all schools a religion-free zone. Those that don't want to go to religious schools don't have to, but for others it can be extremely enriching. It's not religion that causes conflicts, but people's perceptions and approaches towards them, so that's what needs to be fixed.