In a very vague sense in many 19th and 20th century Christian writings when someone talks about "Cartesian" they mean they just mean whatever can be boiled down to the maxim:
I think therefore I am
And like evolution, people get the impression that reading that line gives them all they need to know about Principia philosophiae the same way "Survival of the Fittest" gives them all they need to know about Origin of Species. And because of this:
It has the fatal quality of leaving on many minds the impression that they do understand it and everything else; just as many of them live under a sort of illusion that they have read the Origin of Species.
G.K. Chesterton - The Everlasting Man
Maybe Thomas Merton was writing about something deeper. He was a popular author writing philosophy for the masses, and this, at least probably lends itself to the idea that describing something or someone as Cartesian means branding them a Materialist Philosophy; one that would be banned in happier times (i.e. the Middle Ages).