Either convention will work, since the primary significance of the Minkowski inner product is that for any two four-vectors, its value is invariant for all observers; a change of coordinates does not result in a change in value of the inner product.
Either convention will work. Its value is invariant for all observers. This is for any two four-vectors. The primary significance of the Minkowski inner product is this. A change of coordinates does not result in a change in value of the inner product.