Can the Separatist and Scroll Scholar cleric archetypes be combined?

Question

Each of these archetypes changes something about how the cleric's domains work, and I'm not sure if they can be combined.

The Separatist chooses one domain from those that their deity normally offers and a secondary domain that can be almost anything. For that secondary domain:

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.

The Scroll Scholar gets Diligent Student, which

...replaces one of the 1st-level granted powers from her domains—the character gets to choose which of her two 1st-level granted powers it replaces.

Here are the ways that I could see this getting ruled:

1. The archetypes cannot be combined, because both of them modify the Domains class feature
2. The archetypes can be combined, but Diligent Student has to replace the ability from the primary domain, because that is the only domain power the cleric has at 1st level.
3. The archetypes can be combined, and Diligent Student can replace the second domain's 1st level power, even though the cleric wouldn't normally get that power until level 3.
4. The archetypes can be combined, but Diligent Student won't be usable until level 3 if it replaces the second domain's ability. In this case, Diligent Student functions as if the cleric was 2 levels lower, just like the second domain.

Is there an official way that these archetypes would work together, or are they / should they be mutually exclusive?

Answer 1

Officially, they do not stack...

The answer by william porter describes this well; officially, the slightest change results in incombatibility. Even, say, two archetypes that add—not remove—class skills would be incompatible with one another.

...but this is often absurd

The hardline compatibility rule exists for a number of decent reasons—it eases Paizo’s own responsibility for supporting archetypes by reducing the overall number of official combinations, it provides DMs a strong position to make their own calls without pushback, and it provides the most-conservative-possible approach for tightly-ruled events like Pathfinder Society play.

None of these, however, is “because otherwise it will hurt your game.” None of these is even “because it enhances the overall fun of your game.” All of them are taking an extremely conservative standpoint because it’s easier and lower risk. Paizo is not able to go through every possible combination of archetypes when writing new ones; that would be a monumental amount of work, and their business model relies on cheaply and extremely rapidly producing extensions of the Pathfinder system. The two are simply incompatible, and since they haven’t balanced things around combining archetypes, it’s in their best interests not to make any broad, generalized claims that things should work when their might be an exception. (I mean, they do this anyway, since tons of combinations in Pathfinder are imbalanced, but this is an easy place to reduce it.)

So Paizo simply doesn’t have the resources to consider every interaction and so just says “no” to everything even remotely interacting. But a GM is able to consider every interaction that actually comes up in a game, and a reasonable GM would see that the “incompatibility between these two archetypes is minor in the extreme and easily massaged into place.” To wit: it’s really easy to use your #4 interpretation as a simple, true-to-the-spirit-of-the-rules interaction, and the GM shouldn’t feel too worried about that combination.

There are definitely situations where archetypes really cannot be reasonably combined. But simple cases like this, they can be quite simply, and in my opinion, a good GM should, regardless of what the official rules say (barring PFS or similar where houserules in general are inappropriate). A new GM might not feel comfortable making that judgment—fair enough—but ultimately no GM should feel constrained by the official rules if something seems fair to them.

Answer 2

They don't stack.

This FAQ says:

Archetype Stacking and Altering: What exactly counts as altering a class feature for the purpose of stacking archetypes?

In general, if a class feature grants multiple subfeatures, it’s OK to take two archetypes that only change two separate subfeatures. This includes two bard archetypes that alter or replace different bardic performances (even though bardic performance is technically a single class feature) or two fighter archetypes that replace the weapon training gained at different levels (sometimes referred to as “weapon training I, II, III, or IV”) even though those all fall under the class feature weapon training. However, if something alters the way the parent class feature works, such as a mime archetype that makes all bardic performances completely silent, with only visual components instead of auditory, you can’t take that archetype with an archetype that alters or replaces any of the sub-features. This even applies for something as small as adding 1 extra round of bardic performance each day, adding an additional bonus feat to the list of bonus feats you can select, or adding an additional class skill to the class. As always, individual GMs should feel free to houserule to allow small overlaps on a case by case basis, but the underlying rule exists due to the unpredictability of combining these changes.

Since the Separatist archetype alters the domain class feature, and domain powers are a sub-feature of the domain class feature, you cannot combine it with the Scroll Scholar archetype.