Brilliant questions! I am honored to be the first one to venture a reply.
I think that on principal there would be no need for a list of preordained exclusions. I think that the Elect will Recognize themselves and their fellows. Moving forward from that idea, I think that the ideal situation would be that a candidate would need to physically seek out a member of the hypothetical Order. After a minimum period of say 4 weeks of face to face interactions the candidate could petition the member for admission into the Order. Anyone who had made it this far would be admitted for a probationary period of 6 months. During this time the probate would be tested in various ways by multiple members of the Order. The tests would ideally be physical, mental/intellectual, and magickal. The tests would be failable. It would not be expected that the probate would pass all test but rather that they would demonstrate a resourcefulness and ability to adapt and learn. During this period the probate would be expected to prove a basic proficency in magickal theory and practice. The culmination of the 6 months would be an Initiation that could be passed or failed. I concieve of this as something involving a deep fear in the probate and their ability to overcome it. If the probate passes through the Initiation then they obtain full membership in the Order.
To go a little further: once a member of the Order one would have access to all of the knowledge, writings, and practices of the Order. Nothing would be hidden or kept from members based on degrees. To take an example from the mundane world, if I attend a college I have the ability to audit any class I want, check out any book from the library, study any published paper etc. I might not be able to understand advanced physics as a freshman...but I can read all the books, listen to the lectures, and study the material as much as I want. And who knows, I might understand it. In the same way, all Order material would be available to all members.
To briefly summerize: I think that membership in an ideal LHP School should be based on ability and Xeper. I think that ability and ability to Xeper should be tested and proved, but if one has that ability this is what should matter.
Regarding an individuals past: I am not particularly interested in the specifics of an individuals past. I do not care about criminal records, past addictions, or moral failings. Everyone...or everyone who is worth knowing...has a few skeletons in the closet. The important point, espically as it relates to activity in an Initiatory School, is that one demonstrate the ability to activate Willed change (Xeper) in regard to their past and future. In my opinion it is this ability that should be the upmost criteria for a School.
Thank you UV for this question. I think it is something that those of us who have been critical of the ToS and other groups should seriously think about. If we as LHP practioners look around us and see no School that meets our needs, or no School that we could feel comfortable joining, then I think we should begin to consider the possibility of creating a few new ones.