June 4th and 5th are blockout dates because those are the last two days that the "Southern California Select" annual passports are valid before the summer blockout of June 6 to August 20. Historically, both parks have nearly reached capacity on those final days. It's the only two days in June that all five annual passport types are valid.
Disclaimer: I have an annual pass and have used the resident passes for my wife and kids, so I suspect that my using my AP might have been enough for the gate CMs. I'd like to hear from non-APs if they've had to show ID with resident tickets bought and printed online.