For someone as nomothetic as you, there is only one option: Leave.
I've been in your position. I've, in fact, written a paper (along with @CRoss and @mxyzplk) about different approaches to the rules, titled, "Clerics, Magic Users, Fighters and Thieves: Theoretical Approaches to Rules Questions on the Role-Playing Games Stack Exchange".
This group, as described, is intensely idiographic: they prefer the traditions of their group and their consensus mimicry and simulation of the "real" rather than providing for social trust through codified rules. Your question indicates that you are far more nomothetic: you don't share a mutuality of concern with them, and therefore don't partake of their particular traditions (as they claim are "house rules" but stretch far deeper into their implicit social contract). You also require external sources of imposed trust because you play in many different games.
This is exactly the position I've been in in a number of times.
The thing that will cause the least pain is for you to leave. Sometimes the right answer is, "I'm sorry, folks, but I just can't play your game." I was involved in a D&D game that I'm still bitter about, 3 years after it ended, because I couldn't make this statement. The game was playing fast and loose with the rules and the plot drove all success and failure.
Not only was I miserable, not only am I still bitter, but I count it as one of the primary reasons why I can no longer enjoy D&D 3.5.
Sometimes a game is just not worth it. If there are no mechanisms for establishing trust (i.e. everyone builds a consensus world based on shared rules or tradition) ... then there can be no ludic activities. The group will endlessly revert to "storming" and will enter a vicious negative cycle until something breaks.
Don't let that thing be your enjoyment of the game.
