For Judaism and Christianity the tablets are a real object of sacred history, the physical embodiment of the covenant at Sinai. That is the tradition's claim and it is not in dispute as tradition. What scholarship can establish is again narrow: there is no surviving pair of tablets, no independent attestation outside the biblical text, and no archaeological evidence, and the texts themselves reached their present form long after the events they describe. On these grounds the tablets, like the Ark that held them, are treated as legendary in the technical sense, their physical existence cannot be demonstrated.
Because the tablets were, by the narrative, always kept inside the Ark, they have no separate history to test: wherever the Ark is uncertain, so are they, and they disappear at the same point. There is no rival custodial claim to the tablets comparable to the Ethiopian claim to the Ark, and no object anywhere is presented as the original tablets. The accurate account therefore records a foundational tradition of immense religious weight on one side, and, on the other, the plain fact that no attestable tablets exist, set down here without collapsing either into the other.