The way I have understood (or, more properly, decided, because as you wrote, there is nothing more precise) the rule p 275 is that Associated and Friendly cults are compatible, Enemy and Hostile are not, and Neutral are on a case-by-case basis. My reasoning is based on the descriptions of the 5 categories p311. In the case that concern us (Friendly), the description is: "Even without formal arrangements these groups find each other supportive and agreeable. Meetings are likely to be pleasant.". The term supportive is for me (I'm not a native english speaker and may be wrong) strong enough to allow cooperation to the point of dual initiation. The next level(Neutral) says: "Such cults act according to present circumstance. Trouble may occur, but the spark must be deliberate, not caused by minor squabbles.". The 'present circumstances' is what drove me to the 'case-by-case'. I will not elaborate on the last 3 categories (Enemy, Hostile and Associated) because they seem obvious.
Another point is that I feel that if the author of the rule wanted to have only associated cults to allow dual initiation, he would have written associated, not compatible.