It definitely won't be as bad as Christmas time, but with the 60th anniversary events, it will probably turn out to be more crowded than the previous years were, especially with the AP holders. Before their blockouts, expect large amounts of AP holders in the parks who are trying to squeeze in one last visit before the blockout begins. For SoCal Select APs, the blockout for the summer is the first week of June, while for the SoCal AP's, the blockout is the last week of June (with the dates of June 17th to 20th also blocked out). The deluxe and premium AP holders don't really have an overwhelming effect on the crowds.
As for the grad nights, some people have been bothered by the grads, others not at all. On grad night evenings, try to avoid the extreme rides the teens would like (you can do those in the morning when the most of the grads still haven't arrived) and instead, plan a show, a sit-down meal, or kiddie rides, and they shouldn't be much of a problem.
Since June is considered the summer high-season, you should still expect high crowds, but not something worthy of cancelling your trip for. It isn't the height of the summer, like July, and you will have long hours, practically no refurbs, and full entertainment schedules to make up for the crowding, so as long as you plan accordingly, you wil have a wonderful trip!
