Electrical – Possible to ground-fault protect both legs of a MWBC with two single-pole breakers

What you have is a 240V breaker and circuit. The white is NOT a neutral, but being used as another hot...which is perfectly fine and legal. Newer codes require such a white to be re-marked as a hot.

DO NOT replace ANY breaker with one that is larger. 99.9% of the time the wiring is appropriate for the breaker feeding it. Installing a larger breaker could create a fire hazard.

Land all your MWBCs on a 2-pole breakers NOW.

First, big safety problem. If an MWBC has both its legs on the same pole, it will overload the neutral.

It's important to search your entire panel for multi-wire branch circuits and replace all their breakers with 2-pole breakers. Not two adjacent breakers. A 2-pole breaker specifically.

Why? GE Qline does not have the concept of a double-stuff breaker. It has extra nubs on each of the busbars, to which half-width breakers can clip. Absolutely nothing in the Qline system forces adjacent half-width breakers onto opposite poles. As a result, simply being adjacent does not assure the breakers are on opposite poles.

However, Qline 2-pole half-width breakers are keyed so they can only land on opposite poles. So you must put MWBCs on those. They're not expensive.

What is a GFCI?

A GFCI is a black-box which inputs hot(s) and neutral on its "line" side ... and then it outputs protected hot and neutral on its "load" side.

That's it. That's all there is to a GFCI device. To signify the protected side, I use brown and gray wire in conduit work, but you can do the same by tagging wires with brown and gray electrical tape. Now if that's hard to visualize, look at this.

This is a GFCI device in its purest form: a "deadface" GFCI. There aren't any sockets to confuse the matter. It's very clear that you use this one by putting it somewhere it can serve downstream loads, and connecting two line and two load wires, exactly like the diagram.

Back to MWBCs, you can put a single-phase GFCI device anywhere past a split point. It will protect everything downline.

I don't really care if you get one that also happens to have a couple convenience outlets wired to the LOAD side. Just as long as you know what's really happening.

GFCIs and MWBCs

A GFCI compares current flows on hot(s) and its partner neutral. So in an MWBC, a 1-pole GFCI can only work where the MWBC has forked off a hot and neutral, and neither one will interact again with the other hot.

It's fairly typical in residential installations for an MWBC to fork pretty much at its first junction. Red and white go one way, and black and (same) white go the other way, and they never meet again.

You can install a simple 1-pole GFCI anywhere past the split point. For instance in this drawing, the receptacle (the 8 is a receptacle) is right at the break, and could be nudged a bit so it is after the break, by feeding the right-side "circuit 1" off its LOAD terminals.

Your case...

So your objective is to figure out how your wiring is laid out, and where your branch points are. And then figure out where GFCI's can go in this topology. If you find that part of the circuit goes off in a 2-wire branch (and never rejoins), you can put a GFCI device at the foot of that branch.

So it really boils down to whether you can find a point in the right place in the topology: after a split, but still upstream of the tub lanp/fan. Or whether you can create such a point, and fit a deadface GFCI there. Or a liveface. I don't care ;)

Bathroom receptacle circuits

Most (male) electricians don't get this... but a bathroom shouldn't be plunged into darkness from an overcurrent or GFCI trip, while you're holding a rather hot hair curler. That is simply not safe.

As such it is typical for bathroom lights to be on a different circuit than their receptacles. There is also a rule that receptacles can't share a circuit with anything except loads in that bathroom; or alternately other receptacles in any bathroom.