Sorry for another equivariant question out of the blue:

I suppose the G-equivariant suspension spectrum functor (from G-spaces to genuine G-spectra) is still strong monoidal, in the suitable homotopy-theoretic sense?

What would be a reference for that?

You need to chase it a little bit, but it should follow immediately from the fact that Σ^∞ is a symmetric monoidal left Quillen functor between symmetric monoidal model categories