How to avoid the "risk" of relativism

Although Jayanta and Kumārila at occasion admit the validity of all religious systems (see this post), they are far from accepting relativism.
That Jayanta's approach does not result into a relativistic position is due to its being anchored to the Veda as a fixed parameter, and especially to Kumārila's interpretation of it. In fact, Kumārila's defence of tradition and of the necessity of relying on an authority is very far from the acceptance of any authority just insofar as it is an authority. Insightful, in this regard, is Wilhelm Halbfass' reply to John Taber in Beyond Orientalism (1997):

Kumārila does not simply represent a special kind of traditionalism; he is a fundamentalist. For him, traditionalism (which is characterized by the acceptance of ancestral habits, commonly recognized standards, etc.) is nothing more than conventionalism. To be sure, Kumārila did not have to face the modern specter of relativism. Yet he was familiar with numerous incompatible religious traditions and moral codes, and he faced these traditions as well as his own tradition from the outside. He did not simply advocate what he had received from and through his tradition, but he set himself the task of identifying an underlying principle for his tradition, and of defending it in an open arena of philosophical debate (p. 480).

On Jayanta's approach to other religions, see this post.