I would vote for you folks at Carbine to make the simplest possible changes in the least invasive way, catering to the crowd most likely to benefit from reduced faction barrier.
Ideally this would mean implementing cross-faction housing as a 'first wave' approach. Lore-wise it's grounded in Protostar and begins with a short quest that unlocks cross-faction status, thus allowing players to select whether or not they want to participate. This should hopefully require little effort from you, is player-centric, and caters to builders and RPers as test subjects.
If that goes well and there isn't significant outcry, and you're able to test to see how many people actually participate (by completing the quest), you can implement the second wave, which would be cross-faction PVE instances for expeditions, adventures, and dungeons. This would simply be another quest, possibly again using Protostar as the lore anchor, and would let players select a cross-faction option when queueing. Coincide this with a multi-queue release and a special bag of rewards per clear, to incentivize participation.
Now comes the big controversial part, which would only be released if the second wave proved successful: third wave would be a cross-faction raid queue. I'll offer two options for implementation, the first being a slightly reduced difficulty, the second being the same difficulty with built-in boss mechanic explanations via storyboard graphics (similar to you-know-who's dungeon journal). Either way you could add an incentive from Protostar, or whichever group becomes the third party faction to these changes. It could be a bag of goodies but I would actually go one step further and encourage you to make it a rep-based group that offers a plethora of rewards and a reason to continue running this content weekly.
In all of these cases, PVP should be automatically unflagged upon entry of the instance and prevented for the duration. I see no reason to complicate any of these situations or take up your time recoding a flag system.
I would minimize lore advertisement/development for these changes and focus on selling them as gameplay QOL benefits, rather than being dramatic alterations to your storyline. It's possible to work with the idea of reluctant allies who are only doing this becaues they think that, in the end, it'll help their faction achieve dominance.This would hopefully minimize negative feedback and allow your writers the room they need to continue developing the faction conflict, if such a direction is desired. Arcterra seems like a good platform to justify any changes made, since the factions have effectively become neighbours (and you've got a couple of scientists chatting on the border).
If you feel like investing more time and energy, I'd also recommend coming up with a way to reinforce faction awareness and pride, should you choose to make these changes. I personally don't care for factions but I can clearly see that many people do. Factions provide a 'home team' mentality and create distinction so the game world feels more dynamic. So if you were to push the second and third waves, I would create some way for players to still represent their factions while doing this content: i..e., some kind of meter for each faction that fills based on cross-faction participation, resets weekly (perhaps), and provides global benefits. So at 100 'fuel' collected the Dominion all get bonus XP, then prestige at 200, then EG (to cap faster) at 400, then maybe omnibit bonus at 1000, etc.
Basically, work with faction pride, play on it as a psychological and gameplay device, while also nurturing the desire for faster queues and more diverse group lineups. I don't feel that there has to be a binary choice here.
That's all I've got.
I agree with all of this.
Not only would it be a smooth test drive, it will also be less of a shock to the players, and also less of a strain on the Devs to implement so much.
I'm all for factions, especially as a role player! They play an important part of the lore and it would be awfully jarring to suddenly have peace and rainbows with everybody sharing.
Y'all have put quite a bit of thought into the lore and each faction so it'd be a shame to see such a thing just sort of vanish.
The barriers that prevent people from interacting, however, could be removed but also not take away from the whole war going on between Dominion and Exiles!
Opening up the communication barrier can allow folks on either side to coordinate groups and form them for dungeons, raids, and pvp.
Letting Dominion and Exile characters be able to visit each other in housing can also open up, potentially, housing pvp, and so very many new opportunities for us role players, too!