I attended the Harambe Nights this past Saturday, June 14th - and I have a gluten allergy.
I'll be honest
I don't think Disney handled this very well at all.
I had emailed Disney several weeks prior to my trip regarding this (and other events), but they never addressed the Harambe Nights. When I arrived at the party on Saturday night, the appetizers were set out. I found a CM and asked about allergies; he didn't know, so said he'd have to go find someone who DID know. He was gone a very long time, as no one within Disney seemed to know anything. By the time the Chef came out to tell me what I could have, most of the food was gone and people were lining up for the show.
For the dinner part - it was the same fiasco. I had to find a CM, who then had to find a CM, who then found the chef - and it was a good 30-40 minutes before I knew what was "safe" to eat. Gah.
I happened to be talking to a CM who is a friend of mine on Sunday, and I told her my concerns; I'll probably need to email Disney regarding this so they can address this better in the future.
With that said, the actual show was amazing, and I'm glad I went.