This "shared neutral" circuit is actually one circuit called a Multi-Wire Branch Circuit or MWBC. You must comply with their rules.
Rule: You must pigtail neutrals. You can't use the 2 neutral screws to daisychain through the receptacle as you illustrated.
Shared-neutral circuits must use the same 2-pole breaker
(Okay. There's an exception involving handle-ties. But ignore that, because this segways into a very helpful thing!)
The two "hots" that share the neutral must be landed on a 2-pole breaker. This 2-pole breaker assures common maintenance shutoff (an MWBC rule) and that the hots are on opposite 120V poles (a very absolute MWBC rule).
Protect a shared-neutral with a 2-pole GFCI breaker
As it happens, they make 2-pole GFCI+breakers, which accept 2 hots and a neutral. And that's what your cable is.
You fit the 2-pole GFCI breaker, attach its neutral pigtail, and bring all 3 wires: both hots and neutral to the GFCI breaker. And you're done.
This will fully protect any legal configuration of MWBC/shared neutral circuit. You don't have to worry about how neutral is shared and firewalling line from load. It just works.
"Oh, but 2-pole GFCI breakers are expensive" -- so are four GFCI+receptacles, as you show in the drawing in your edit.
If you must use many GFCIs - just don't use LOAD
If you absolutely insist on using GFCI+receptacle devices, well.... okay. You can do as in your last drawing (in your edit).
This makes it a very simple rule: Don't remove the warning tape from the
LOAD terminals. Simple as that. Of course, you'll be sitting there tempted, right? 2 wires in your hand and 2 screws you can't use--- nuh uh don't touch that tape! You have to figure it out another way. Hands off!
This will lead you to a concept called pigtailing, which I remind you, you need to do with the neutrals anyway because of MWBC rules. So, now you're doing it with the hots too. Pigtail every connection onto the
LINE hot and neutral, and voila. You have GFCI protection everywhere you choose to fit a GFCI+receptacle. And it didn't explode your brain.