I recommend that you use like materials.
I agree. My house is 68 years old and was built using the old BX cable, with no grounding for the outlets and no bonding strip in the BX. There's just no way I'm going to try using Romex to extend or add circuits to that system. I recently added a couple of circuits, and I used MC, which has a green ground conductor in the bundle. I used all metal boxes, so all the new work is compatible with the original installation.
Reading what the code says, I may have been incorrect and it may be code-compliant to connect Romex to a BX system. But the code doesn't say you can or can't -- it says the armored cable (BX)
"shall be installed in a
manner that creates a low-impedance circuit facilitating the
operation of the overcurrent device or ground detector for
high-impedance grounded systems. It shall be capable of
safely carrying the maximum ground-fault current likely to
be imposed on it from any point on the wiring system
where a ground fault may occur to the electrical supply
source."
How to verify what constitutes "low-impedence" or "safe" when you use Romex to extend an old BX system is above my pay grade.