I think that is a key difference between modern christians and modern muslims, the christians are more "interpretive" and will ignore certain parts of the bible that clash with modern sensibility whereas muslims don't do that too much with the quran. But if you trace christian history it used to be the same way muslims are today so maybe future muslims will be more "interpretive" like modern day christians and come to ignore certain parts of the quran that may clash with the societal values at the time.
I don't think you really understand the history of christianity, otherwise you would have known that reinterpreting jesus' message has been done by christians since the early years right after jesus was raised to heaven. Modern day christians who you called "interpretive" merely continuation of christian tradition who have to keep reinterpreting and twist the bible to conform with society attitude of the day, from paul's attempt to make jesus teachings to be more palatable to the greeks to roman emperors sanctioning certain sects of christianity to medieval roman catholics to protestantism/reform all the way the present day christians who go bend over backwards to appease modern living including gay marriage etc.
And this all happened because jesus message was not properly and strictly preserved and recorded when he was alive, and then totally destroyed by paul, who never met jesus, who claimed that he received divine guidance in his dreams and totally abrograted jesus' teachings and raised him as god.
since then christians think that as long as they accept jesus as their savior, everything else does not matter and they will go to heaven, hence you will get mainstream christians who will try to fit christianity into society all the time.
Meanwhile, contrast that to muslims who believe that the Qur'an is the direct speech of God, which is 100% preserved and stays intact from the time of the prophet SAW until now where millions of muslims memorize completely the Qur'an, as well as the hadiths, collection of the prophet SAW sayings and actions which are preserved with 100% transmissions known along with the credibilities of the transmitters.
Since the time of Rasulullah saw, mainstream muslims (ahlusunnah al jamaah) hold fast to the Qur'an and hadiths without trying to "reinterpret" and/pr twist the meanings.
You will always have fractions and sects who will keep trying to do otherwise, however.