Variant channeling comes from ultimate magic. It is described there as an "alternative effect" and it is never called an archetype.
The archives of nethys has that section of text under variant channeling pretty much identical beyond some formatting stuff. It is still not at all mentioned as an archetype.
Archetypes have certain rules when you choose one, and when you choose to stack multiple ones. Of note here,
"A character who takes an alternate class feature does not count as having the class feature that was replaced when meeting any requirements or prerequisites."
"A character can take more than one archetype and garner additional alternate class features, but none of the alternate class features can replace or alter the same class feature from the core class as another alternate class feature."
Of course, that first quote IS specific to abilities that are replaced and not simply altered, and there have been a few faq's that might touch on any given ability as well.
The second one, the one that limits replacements and alterations, is specific to other archetypes - not other optional alterations that you may be able to apply to any individual class feature.
So there are no specific rules that prevent them from working together. A couple notes on some of the examples above though - bloodline mutations CAN work with an archetype. The caveat is that you cannot swap a bloodline power that has been altered or replaced with an archetype for a bloodline mutation. You could still swap an unaltered power, or a bonus bloodline feat for a bloodline mutation.
Similarly, you can take advanced versatile performances with an archetype, as long as that archetype isn't altering or replacing versatile performance specifically.
Wildblooded is an archetype, so it stacks (or doesn't) following the normal archetype stacking rules.
One thing to keep in mind though is that if an archetype replaces channel energy or significantly alters it with specific limitations, then the variant channel options may no longer be applicable. For example, the Idealist cleric invoke realm alters channel energy in such a way that you are not channeling positive or negative energy - which negates variant channeling.