And if so, how hard would it be? Would one have to decline every mission (storyline or not) that is against faction navies?
it's quiet easy, just reject missions against a faction then you wont lose standing with it. the best you can do is: find some agents that are close to each other so while you wait the 4 hours until you can reject a mission again (in case you have 2 anti faction missions after one another) you can go to one of the other agents and do missions there. also if you just want to grind standings, use an agent who has mostly courier missions.