Soltair,
I'm not sure I understand why cultural influence would change while at war. From what I can tell from the manual culture is tied to things unrelated to military production. Being at war with an enemy does not remove the desire of the populace to receive the cultural goods (i.e. music, ideologies, goods, etc.) nor the ability to receive them.
War does block the ability to receive them legally (i.e. government regulated and taxable). In the absence of legal ways to receive these goods, black markets will evolve that will supply these to the other empires.
War also doesn't prevent the other empire from atempting to empathize with the opposing side nor attempting to defect because they tend to agree with the other side.
As for the cultural resistance, it appears to be slightly built into the model in a somewhat backwards sort of way. Improving the government type reduces the effect of morale on limiting population growth (at least according to the techs). Larger populations have lower morale, lower morale planets are more likely to defect.
As for the starbase issue... I'm not so sure. An influence adjusting starbase in your area isn't really an act of war. If their culture is getting too big in an area there is always the option of fighting fire with fire (i.e. build clutural starbases of your own).
Without borders it is hard to differntiate between who "owns" an area of space. The influence map, to me at least, doesn't correspond to actual borders but rather who is making themselves heard the most.