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.
The two bonus fast pass deal that now offer disney for each guest for stay of disney hotels are valid from january until june 10, that can be another signal.