This answer from SE says it's not possible to prevent auto-protection on a specific question, and adds:
If you can think of better guidelines for when auto-protection shouldn't be applied and why
How about this: if the question has been unprotected at least N times (2? 3?), then don't auto-protect -- the community is clearly saying "leave this open to new answers from anybody".
This approach depends entirely on the post history and not some new status field (and UI). Post history also affects some other actions (can't migrate a migrated question, can't undelete a mod-deleted post, don't display post text if deleted by spam/offensive flags, maybe others), so looking at post history for protection is consistent and doesn't require schema or UI changes.
Shog pointed out in a comment that this proposal would interfere with protection for sudden popularity. So here's an alternate proposal: when considering the first case, "3 answers from new users deleted", only consider deletions that occurred soon after the post was made (within a day or two?). If an answer from a new user was allowed to stand for a month before anybody sought its deletion, how harmful was it?
We have run into a problem with auto-protection on Worldbuilding, where we (like PP&CG) have a sandbox. Ours currently has 32 deleted answers. The author of several of them had his rep drop to 1 a few days ago, and as a reult it's been auto-protected twice. (This prompted me to ask if that should happen.) We want new users -- including low-rep users whose rep can be volatile -- to be able to refine their questions in the sandbox before posting on main and having a bad experience there. These are exactly the users who are blocked by protection. Sure, we can keep playing whack-a-mole; somebody usually notices within several hours, maybe a day, that the question has been protected again. But can we remove that barrier? (I'm aware that this particular case has other factors in play, but I think the general point remains valid: deletion by itself doesn't mean the answer was bad; prompt deletion is a much stronger signal.)
I'm aware that we could turn protection off on our meta entirely, but (1) I'd rather solve the problem more locally and (2) that doesn't help with unwanted auto-protections on main sites.