I think both 1 and 2 would be a good idea, even if you can only skip after meeting them, than there should still be a warning that you could miss important things like birthdays, special date events etc.
Also it doesn't take too long to meet them all, so not being able to skip until you have met them might help give people set up their play through and think about some things before getting overzealous about skipping.
To be honest I would love a skipping option. Sometimes I get to a point where I have maxed the lovers heart, unlocked most of the cut scenes, done all the side quests and reached superstar level but it's still weeks/days till something interesting happens. Especially now that I'm doing Keade's route got his last cut scene in May, I have no idea what I'm going to do after I reach superstar level.
It also might be a good idea to only make the skipping option available after your first playthrough.