Maybe one way to discuss this is;

1) Suppose that you have an 'edison' (split) outlet. Assume for the
moment it is, say, inside the house.

2) Beyond, i.e. further downstream of that, and for use outside, you
install two duplex GFCI outlets. One of them uses one of the 120 v legs
and the neutral. The other uses the other leg and the neutral. The
neutral splitting 'before' going separately to each GFCI. The neutral
cannot 'go through' one GFCI to reach the other.

3) Anything plugged into either of the GFCI which causes an unbalance
of the neutral and live wire currents flowing to/from that outlet will
cause it to trip and protect. The other GFCI will not trip.

4) Even if one or both of the GFCI operate, the edison outlet will
still be fully live on both parts of its split personality. In fact
after installing the two GFCI you could eliminate it! Or not install it
all in the first place?

Assuming the edison arrangement and two GFCI outlets are needed because
of an expected larger load than the 15 amps that can be drawn from a
single duplex outlet (GFCI or otherwise)? If not one (non edison) GFCI
outlet could be installed and a 'regular' outlet downstreamed from
that! Both would be protected by the single GFCI.

BTW I came across an older GFCI of the type that does not allow another
outlet to be downstream of it. So installed it in a metal box at the
end of an older but substantial extension cord. This provides a GFCI
protected circuit no matter where plugged in; for example can be
plugged inside the house into a regular non GFCI outlet and run out
through a window to work on something outside.