Trust as a principle does not mean blind trust. It means trust as a default attitude. Trust as a universal default is perfectly compatible with every kind of critical thinking.
When we trust someone, we grant them a kind of authority, but authority must always be balanced by symmetrical responsibility. To make any assertion at all is enter the space of reasons. To make an assertion is to make oneself responsible for it, along with its consequences and incompatibilities. No one has privileged access to what is right, which depends upon shareable criteria. Generalized trust does not mean naivete or credulity, just a kind of fairness. It could not mean an abdication of our responsibilities as rational beings. In the context of what Brandom would call deontic scorekeeping, generalized trust means a level playing field, not an absence of standards.