I only ally with neighbours I don't want to attack, or neighbours of neighbours I do want to attack. The rest can take a hike as far as I am concerned. Just because they want an alliance doesn't mean they like me: especially Takeda is known to offer alliances and break them the next turn. I almost always grant emissaries an audience though; no need to antagonize other factions unnecesarily. Then I attack the faction that forms either the greatest threat or the provinces that come with the greatest rewards (not always money, security on one flank is very valuable as well). I do not let the other factions diplomatic stance dictate my actions, and will only seldom be disuaded from an attack by the diplomatic fall-out.