The principle of non-contradiction is not a provisional postulate, it is a necessary truth based in reality. If it isn't, we are screwed. Our science is about cloud cuckoo land, not reality. Logic is ontologically prior to the material world. Reality is fundamentally intelligible, and at the foundation of everything is a rational, not a material explanation. Even the philosopher Thomas Nagel, who is careful to avoid any theistic implications for this line of reasoning, realizes this.
If you say we agree to the convention, that implies we could have done otherwise. We can't. We bump up against reality, not our own rules, when we do so. When we agree to conventions, we could have done otherwise. When we are facing reality, we cannot do otherwise without, well, scraping ourselves against reality.