Except the 1st doesn't trump the 4th.
Within your own house (or other private area), you have a right to control access to allow for a reasonable level of privacy.
That is, allowing you to walk into my home does NOT automatically give you the right to record everything you see there. As the owner, I retain my personal rights to everything there; your rights don't trump mine, because this is MY private space. This also applies to actions within that space with respect to the guest: the homeowner does NOT automatically gain the right to record the guest WITHOUT permission.
Similar protections apply to all places where a reasonable expectation of privacy exists: bathrooms, private hotel rooms, etc.
A minor level of Prior Restrain is perfectly reasonable here - that is, the owner must show PROOF of permission for photographic reproduction, since the possible harm from an illegal post outweighs the benefits of unfettered postings. That is, documented permission from the participant is NOT an onerous burden on the poster, and, in fact, protects the participants' 4th and 1st Amendment rights, which, in this case, are reasonably seen as being greater than the picture owner's.