When I've been part of shows where a behind-the-scenes video (or Instagram takeover or similar) was created and used for promotional purposes, we followed the terms of the AEA contract. In LORT, for example, there are rules governing the duration of footage, the timeframe for notifying involved parties, the way in which the footage is subsequently stored or re-used, and more. Each contract may have unique stipulations, so legality in this case is murky if you're seeking an industry-wide policy. I am sure that some producers have explored ways to add contract riders that would preempt disagreement from AEA company members regarding backstage footage, but there's no way to know if these riders made it out of discussions or what clauses were inserted, absent a ton of digging around in polls and phone calls to AEA.
It seems like your post touches on two questions: first, a moral (or perhaps ethical) question about revealing potentially intimate, personal moments offstage; and two, a question about adherence to the relevant labor contracts and state laws that may impact the words, images, etc. that are rightly intellectual property. Is this interpretation of your original post correct?