Sooner or later this difference will really start sticking out when you inevitably reach some 'bigger' decisions that have to be made together. It doesn't really make a difference in casual dating or short-term stuff.
For example, imagine something more long-term develops and some decisions like buying a property, car or whatever have to be made. If you have a significantly different approach to decision making(irrational vs irrational), it will take enormous effort to reach a settlement, compromise or sometimes it'll be entirely impossible. Sometimes you will
know you are entirely in the right especially if it's a conclusion that can be logically reached. But how do you appeal with reason to someone that doesn't rely on reason as a decision making factor nearly as much as you do?
If you're lucky, you're more or less compatible and willing to overcome these issues together but as you know it takes time, a lot of time, for someone's character to fully surface. What seems like an odd quirk here and there almost always stems from the core beliefs and if you aren't very compatible in that there will be issues. There are of course degrees to this so it's just a matter of how much you're willing to compromise on.
Personally, JFK would be fine but aliens would not be