Logic in two different directions
Both decide with thinking, but they point it in opposite ways. The INTP uses introverted thinking (Ti): does this make sense, internally, all the way down? The ISTJ uses extraverted thinking (Te): does this work, on time, in the real world? One is checking the blueprint; the other is checking that the house got built.
This is why early conversations can be satisfying. The ISTJ brings facts and experience, the INTP brings theories, and both enjoy a debate that stays reasonable. Neither needs constant attention, and both are comfortable with long, companionable silence.
Tax season
The ISTJ has a folder for every year, labeled, and files in February. The INTP has receipts in three jacket pockets and has spent an evening reading about why the tax code treats home offices the way it does. In April the ISTJ is anxious and the INTP is fascinated. Each starts privately filing the other under a word: the INTP thinks rigid, the ISTJ thinks unreliable.
The same shape shows up in smaller ways. The ISTJ has a system for loading the dishwasher. The INTP questions the logic, designs a better one in their head and never implements it. The ISTJ wants the plan kept; the INTP wants the plan justified. Both may feel the other is impossible to live with, when really they’re answering different questions.
Neither finds it easy to say how they feel, so these frustrations can sit unspoken until they come out as a list of complaints.
Reasons for the routines
An INTP will follow almost any system they understand. So the ISTJ can explain why a routine exists (“we pay on the 1st because the late fee is steep”) rather than only that it does. In return, the INTP can commit to a small number of concrete deadlines and treat them as non-negotiable.
Give the INTP unstructured thinking time that the ISTJ doesn’t schedule over, and give the ISTJ a heads-up before any change to shared plans. Both can practice saying one appreciative thing aloud each day. It sounds small, but for two reserved people it changes the feel of the house.