I think Rhiannon has made several excellent points here.
The long and short of it basically being that if you choose to be involved with null-sec living and also RP you just have to deal with the elephant in the room of whatever non-rp sov power block is in your way. Plenty of opportunity to make something fun out of it for your character and their friends.
In many ways, you can even treat them like NPC factions. They never RP, they never post on the IGS, so you do have a nice advantage of being able to fashion stories/plotlines that take that into account.
In Space: You are still able though, to use events in space to further your ideas. Shooting down a few goonswarm ships or an IT pet capital ship still happened in space, so it seems perfectly valid to incorporate that into your RP. That the entities you are fighting/destroying aren't going to interact back with you IC is unfortunate, but ce la vie.
Out Of Space: I think there's plenty of room for one's own world-building on planets/colonies in the NPC 0.0 areas, and so long as you've thought it through well enough, even in territory owned by non RP alliances.
For example, my alliance is currently out in Querious shooting it up with IT and several of their pet alliances. There's plenty of exciting things going on that I'm in the process of working into some stories, etc, and I toss a little IGS thread out occasionally with some of our happenings. I'm restricting myself to things that actually happen in space though, until we've actually conquered anything. I can't write about subjugating the heathens in 0.0 unless there's been some subjugating in space to back that up.
I feel once we take any systems, or take a station, that I will have earned a little RP lee-way and be able to produce some fun fiction incorporating those events.
An example of this would be conquering a player built station in null sec. I think it's perfectly reasonable to assume that a few hundred capsuleer ships, including a massive capital fleet, incorporates many thousands of crew and combat shock troops for a station boarding action. I imagine sieging and taking control of a starbase would involve a lot of serious close-range combat by the grunts. Securing hangars, door to door assaults, that kind of thing. A major 0.0 alliance would have many thousands of people inside a starbase, and I think safe to say they would not just 'get up and leave' and leave the lights on for us to take an empty station. Especially if the station is being blockaded, it adds extra weight for there being a major 'fight' inside the station.
Did this expressly happen in the game? No, but if I own the station after taking it from someone else, change the name to "Khanid Family Refinery" or whatever, I feel I've earned a bit of RP leeway to make it an interesting story.
This applies to any number of other scenarios, so high-sec empire RPers should have a whole world of fiction and IC happenings to come up with. Maybe some Amarr RPers could run out to blood raider territory and launch some attacks, maybe some Gallente researcher could come up with some interesting storylines out in the drone regions. Maybe a Caldari business-man can write about some events going on in hone of his PI colonies out in 0.0 somewhere. There's a million ways to go, only limited by our creativity.