Finally reached 8/12 with Moon, but i still don't guess which day is the one for trigger her storyline. In the meantime i'm dating all the girls for rise the affection: i noticed only now they were all under the 30 value. And i bet, in the next update, if i want to progress in certain storylines, i'll need at least a value over 45 points or even more.
No, you don't 'need' anything, the only thing you have to raise is the relationship level, that is just a tracker to show how many story events you have done with them. So that is not a 'stat', it's just telling which event you are on.
A few scenes have requirements for some extras, but they are not that important.
The one exception to this rule, is Lin, and her contest event, you want to win, and to do that, you need a 10 in most of her sex stats (BJ, Vag sex, and Anal, IIRC). And of course, the Exhibitionism stat can unlock some extras here and there, so I would raise that, if you like that kind of thing.
But there is not one actual stat that is required to do anyone's story, and I don't think any of them need to be over 10, 20 tops for the bonus stuff. I don't expect that will ever change. The game used to show us improving up to 50 in the bars, with the star levels, but that was removed, and now it's just 1-10 (or less on some).