I don't know who you are calling "fundamentalists" – I personally think the term should be restricted to the historical fundamentalist movement in American Protestantism, and those Protestants who view themselves as heirs of that movement today – but I think the vast majority of people you are labelling that aren't theonomists, and have zero interest in emulating Islamic Sharia by replacing secular courts with tribunals of Christian clergy, or modifying evidence laws to make the word of a Christian worth more than that of a non-Christian. Nobody is asking for anything remotely resembling that, except for a very tiny movement on the fringes of Reformed Protestantism – which the vast majority of Reformed (even conservative Reformed) reject, and I've never heard of a Catholic or Anglican or Methodist or Lutheran or Eastern Orthodox or whatever supporting it.

From a Catholic perspective, replacing secular law with "Christian Sharia" is clearly a heresy – never officially condemned because no Catholic of significance has ever proposed it – but if it ever did become a serious issue I'm sure the Church would waste no time in doing so, since it is just so blatantly contrary to the Catholic tradition. And the Eastern Orthodox Church, and the vast majority of Protestant churches (even otherwise very conservative ones), would say more or less the same thing – the details of their reasons would likely differ, but the conclusion wouldn't.