GFCI Install with 2 circuits
Don't use the words "line" and "load" for plain receptacles. 

What's happening here

If indeed the power is coming from the upper right... This is a multi-wire branch circuit that appears to irrevocably split here.  It shares neutral up to this point, then it does not.   

Because it is an MWBC, the neutrals are pigtailed.  That is correct and important.   However it is not necessary after the MWBC hots split for good, so the upper left cable did not need to be pigtailed, it could have chained off the receptacle same as its "hot" does. 

The lower right cable is the "red" leg of the MWBC.   It departs and we don't deal with it again here.  

The receptacle is the "black" leg of the MWBC.   

How to hook up a GFCI

It goes without saying that you de-energize both sides of the MWBC before doing anything with wires.  This will involve many trips to the breaker panel.   Most likely the breakers are adjacent, possibly with a handle tie, or are a 2-space 2-pole breaker.  

First, disconnect and fold back both hot and neutral from the upper left cable.  We will not be using them at all. (yet.)   You might, at this point, go see which receptacles are downstream and now dead.   Make a note of those.  

The lower right cable stays exactly as it is.  

At this point there will be 1 hot and 1 neutral going to the receptacle, and the receptacle should work. 

Replace the receptacle with a GFCI type.   The hot and neutral go to the LINE terminals.   The LOAD terminals are unused.   

At this point the GFCI should work fully.  Plugging anything into any receptacle in either this or the other half of the MWBC should not trip the GFCI at all.   A GFCI test on the other half of the MWBC should not trip this GFCI.  

Lastly, go back and grab the upper left cable I said we weren't going to use.  Connect these to the LOAD terminals on the GFCI.   At this point all the downstream receptacles should be back up.    Now go test the downstream receptacles with a GFCI tester.   All should trip the GFCI.   Other than that, if you are now getting nuisance GFCI trips, it means one of the appliances downstream (or the wiring) has a ground fault (that is, after all, what you are paying this gadget to detect).