Installing GFCI outlets in multiwire branch circuit
This type of shared-neutral wiring is called a Multi-wire Branch Circuit, or MWBC. 

All these issues are entirely mooted in your case, since you will not be able to use the LOAD terminals at all.  There's simply no way to do it.  You only have two receptacle sites per MWBC.  The whole point of an MWBC is to make good use of both hot legs.   Well, you need two GFCI+receptacle devices to do that.  And that fills both sites.   So the issue of extending off the LOAD terminals of one of the GFCI+receptacles will never come up.  

A GFCI that doesn't use its LOAD terminals can't have a shared neutral problem.  

Scenario 1:

As you propose, in box 1 of each circuit, connect the GFCI+Receptacle device to the LINE terminals only.  Connect black and neutral, and cap red.    In box 2, cap the black and comnect red and neutral to the LINE terminals.  And you are done.  There is no use for the LOAD terminals, leave the tape on them. 

Before, the 8 sockets went to circuits as follows: 1.2------1.2------3.4------3.4

Now, the 8 sockets go to circuits as follows: 1:1------2:2-------3:3------4:4

Keep that in mind when plugging in heavy draw appliances.  I.e, it's no longer "pick one socket, 1 on top 1 on bottom", now it's "1 appliance per GFCI". If you liked the other way, see Scenario 2. 

Now, if you need AFCI protection, you need the newer cAFCI breakers designed to work in MWBCs, that do not need the circuit's neutral wire landed on the breaker.  (the AFCI may have its own neutral pigtail, this is only to power itself.) These are all 1-pole breakers, so you will need a listed handle-tie to tie them together so they are shut off together for maintenance.  This will resemble a 2-pole breaker. 

Scenario 2

This depends on not needing AFCI.  

In this case, you leave the wiring exactly as you found it. You will then replace those 2-pole or handle-tied breakers with 2-pole GFCI breakers. In this you land all 3 wires (2 hots+neutral) on the GFCI breaker. You cannot handle-tie two singles because of the shared neutral.  

If you can find a 2-pole cAFCI+GFCI+breaker device, you can use that.  I haven't been able to find one.  



As far as the answers you're not understanding, Tester101‘s postings are sublime, among the finest on the forum. There's a lot of technical data there, and the volume of material makes it confusing when these concepts are new.  I see no conflict nor contradiction in what he wrote. 

About neutral sharing, he means in the context of MWBC and protecting downline loads using the LOAD terminals.  You cannot.  The one neutral can't be both the Load side of the black subcircuit and the line side of the red subcircuit. Thus, GFCI receptacles on MWBCs cannot protect downline loads, their LOAD terminals are useless.