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.