The MKL blas/lapack implementation also provides the “cblas” interface (I’m sure most blas implementations do, I’m just familiar with MKL—BLIS seems quite willing to provide additional interfaces to I bet they provide it as well) which explicitly accepts arguments for row or column ordering.

Internally the matrix is tiled out anyway (for gemm at least) so column vs row ordering is probably a little less important nowadays (which isn’t to say it never matters).