Legal for Pathfinder Society? I don't know, you should probably ask in their forums.
Legal for an unchained summoner to take outside of PFS? Absolutely. Every single chained summoner archetype printed before pathfinder unchained came out is compatible with unchained summoner.
appears fine. The Unchained Summoner archetypes listed on Nethys are just the Unchained Summoner-only archetypes; the ones that work for both are listed under chained Summoner. Not clear how you are intended to verify that one works, other than know the...policies.
Finally, with the exception of the monk, these classes should work with any of the archetypes from previous books as long as the classes still have the appropriate class features to replace.
The Unchained Summoner has all the class features that Naturalist replaces, so it works.
