Fair, then showcase how it would happen.
After all the solution is to remove double-dipping first and foremost. Because that creates a inherent inequality and goes actively counter to keeping the systems contained in themselves.
So that’s the first step and needs to be done anyway.
Including tradeable items dropping from CoF and Gold used as a currency in MG.
So that’s a ‘given’ without the faction change already.
Next up, the current system already causes a inherent inequality for switching.
That obviously needs to be solved.
CoF has a inherent downside moving to MG compared to MG moving to CoF.
The baseline to achieve that would be ‘wearing a full outfit of non-tagged items’, right?
MG acquires items through the market, extra to the base drop-rate.
CoF on the other hand upgrades items from the base drop-rate into better versions. Or duplicates dropping items.
That means CoF gets less non-tagged items overall.
Obviously not a situation which is allowed since the mechanical conditions need to be exactly the same, otherwise we can’t even start thinking about adjustments as all is intermingled and hence breaking things left and right and causing issues. Bad design simply.
So that needs to go anyway in some way… and now… ‘ooff’'… since that can’t go.
Doomed if you do, doomed if you don’t already.
Hence solely on that factor alone the faction change mechanic is already unfair. Sucks a lot.
Now we can actually come to the things I suggested, to see if it would be ‘fair’ or not.
First off… allowing both factions to keep wearing their tagged gear afterwards.
Obviously creates sudden immediate problems, loads of them even! What holds you back from switching now? Nothing.
So to do that we need a alternative system which doesn’t affect people differently.
That’s why I chose ‘Favor’ for it. Both factions acquire it at the exact same rate after all. What they do with it is open to the individual.
So now we have a situation which removes the unfair treatment between factions, actually removes the punishment itself… but it still costly if the relevant effort is put into changing a faction.
Because you’re right, as Mike wrote:
You’re ‘bricking’ your character a lot harder when you play a while in a faction then when you’re early on.
By the time you feel like you’re reaching a dead end of some kind (be it MG or CoF, both have them) you’re already so far inside that it does exactly that… actively.
Kinda a big ‘ooff’ again.
Sure!
It’s a nice lore reasoning.
Well… if it would count for the character itself. But Favor is acount shared and not individually achieved. That ruins this whole premise.
Instead of punishing the one ‘scorning’ them (entitled pricks btw… you’re doing work for them and when you want to move on they’re being assholes… just sayin) and suddenly they punish you… your mother, your father and your family to the 8th degree! 
Actually kinda hilarious! But sadly bad design still.
Also fairly interesting:
If you create a mechanic the player isn’t supposed to interact with… then you’ve actively failed as a developer. Not even a question there.
I mean, it’s intended as a fail-safe, right?
Well… in which situation would you actually ‘brick’ your character through the faction? And in which situation would it actually be more detrimental then a following switch?
If you missclick… wouldn’t a… lets say 1 day cooldown timer for a one-time change be sufficient?
What else exists beyond for bricking?
So it’s utterly overengineered and missplaced simply. Still… bad design overall.
Mission successfully failed I would say.
Please finally keep the whole sentence together as a single context.
Cherrypicking is for a reason nonsensical… you can twist and turn everything willy-nilly how you want. You can’t state anything without it being dismantled into nonsense and entirely different to the initial notion.
No, since when you read the whole sentence it’s not anymore.
So… can you finally move past it? That won’t change.
Are you acruing 100k favor every day hence?
If so… how much beyond will you acrue? So will it actually provide you a overall upside or downside as a end-result?
Please stay in the provided framework. If you make your own obviously things don’t work as intended
That’s quite clear.
Are you loosing something by not doing it?
If so what would you loose in comparison (mind the framework), or what would the other side gain? (mind framework again)
Don’t worry, there’s better things as reasoning available 
Albeit I’ll also mention that ‘abstaining from using a mechanic’ is generally psychologically harder then ‘abstaining from not using a mechanic’. The artificial reduction of options has a higher mental difficulty then the increase in options beyond the active scope. But that’s not part of the topic, just a side note.