So Apocryphal subdomains require a trait to take normally but the Separatist archetype allows you to pick one that is not normally available. Does the Separatist allow you to bypass the trait requirement?
Forbidden Rites: A separatist selects one domain from her deity’s domain list, and a second domain that is not on her deity’s domain list. This second domain cannot be an alignment domain that doesn’t match the cleric’s or her deity’s alignment. For example, a lawful good separatist cleric of a neutral good deity cannot choose the Chaos or Evil domain with this ability, but can select the Lawful domain even though her deity isn’t lawful.
Granted powers from the cleric’s second domain function as if the cleric’s level, Wisdom, and Charisma were 2 lower than normal (minimum level 1) in terms of effect, DC, and uses per day. This also means the separatist doesn’t gain the domain’s higher-level ability until 2 levels later than normal. If the second domain grants additional class skills, the separatist gains these as normal. In all other respects, this ability works like and replaces the standard cleric’s domain ability.
Going over the wording of the Apocryphal Subdomains, even with the Seperatist Archertype, you need the trait to select one of those subdomains.
Apocryphal SubdomainsA divine spellcaster who studies an apocrypha, or who studies under a scholar well versed in such a text, can gain access to unusual subdomains associated with a deity. Whether or not the mainstream church accepts any one apocryphal text as canonical or not can vary, even within the same religion; for some believers, though, these words are as true as anything about their belief. A domain-using PC can gain access to one of these subdomains via the following faith trait. An NPC does not need such a trait, provided that the NPC has a flavorful background that explains how he or she came in contact with the apocryphal information. Subdomains were introduced on page 86 of the Pathfinder RPG Advanced Player’s Guide.
Acolyte of Apocrypha (Faith): Your religious studies hinged on teachings rarely recognized by your faith. You can select one of the apocryphal subdomains detailed below, provided the subdomain is associated with your patron deity. In some cases, you can select a subdomain associated with a deity despite that deity not offering the associated domain—these exceptions are noted with an asterisk (*), and you gain domain powers and domain spells from the associated domain as usual, even though your deity normally doesn’t grant access to that domain. When selecting a subdomain associated with two domains, a priest can choose only a subdomain that modifies a domain to which he has access. All deities referenced in the following subdomains appear in Pathfinder Campaign Setting: Inner Sea Gods or Pathfinder Campaign Setting: Dragon Empires Gazetteer.