Its viability depends on external factors
It is mostly viable, actually the only viable ranged Barbarian build in my opinion1.
The external factors are:
- party composition
- available space
- encounter type (if it is a single boss, or many smaller monsters)
- enemy type (if it uses attacks)
When I played this build, it was quite useful when everything was optimal.
However, its usability decreased significantly with one of these factors missing.
Party composition
As mentioned in the comments of this answer, this tactic is only good if your party members can keep the target of your Ancestral Protectors (Target) away from you.
Either they have to physically hinder its movement, or discourage it with threats of Opportunity Attacks.
You will want to have at least half of the party members to be in melee.
When the Shield Master fighter was not present at our encounters, my Barbarian worked a lot worse.
Available space
If you fight in a dungeon, sometimes you just can't get far enough from the target while maintaining line of sight.
Encounter type
If there are lots of enemies, you might get far enough away from the Target, but his comrades still might be adjacent to you, causing disadvantage on your attacks. You have to hit your target to trigger Ancestral Protectors, so this can be a big problem for you.
Enemy type
If the enemy does not use attacks, only breath weapons or spells, Ancestral Protectors become irrelevant. Unfortunately the resistance is only against his attacks.
Conclusion
It is not viable for dungeon crawling with a party of 4 Sorcerers, but with the average party in the average encounter you will do more than fine.
Recommendation
Use a Hand Crossbow instead of a Longbow and multiclass to Rogue instead of Fighter.
Hand Crossbow
With the Crossbow Expert feat you can attack without disadvantage even if you are adjacent to enemies, negating the worst consequences of a tight space and many smaller enemies.
When you already have the feat, Hand Crossbows give you the most DPR .
Rogue
2 levels of Rogue make Disengage a bonus action, very valuable in tight spots.
Also a Rogue Multiclass provides better DPR increase than a Fighter2, and this area is where you are very much behind a usual Barbarian, as you can't use Reckless Attack and the damage increase during the rage.
1 Being at range gives you extra survivability, by making it harder for others to target and hit you. Ranged characters come away from most fights undamaged in experience, so resistance is mostly wasted on them, and no other significant Barbarian features are usable at range. Other ranged Barbarian's usefullness in combat is below that of a Ranger, and they are famously weak.
2 A single level of Fighter might still be a good idea for Archery fighting style.
The cleric takes 9 damage
To start with, resistance takes effect after all other damage reductions. So the 24 damage is reduced before resistance is considered. This rule can be found in the Combat chapter of the Basic Rules:
Resistance and then vulnerability are applied after all other modifiers to damage.
After the damage is reduced to 18 (Xd6 = 6 in this example), it is halved to 9 from the resistance granted by warding bond. The cleric then takes the same amount of damage:
each time [the target] takes damage, you take the same amount of damage.
Best Answer
Vengeful Ancestors does not apply to Area of Effect Damage
... because an area of effect spell is not an attack. And Vengeful Ancestors only kicks in when you use Spirit Shield to "reduce the damage of an attack".
The PHB on page 194 says this about how to determine if something is an attack:
For an Area of Effect spell like fireball you do not make an attack roll, hence it is not an attack.
So yes, you can use Spirit Shield without triggering Vengeful Ancestors: Spirit Shield works against any kind of damage. Vengeful Ancestors only happens if the damage is from an attack. If its not from an attack, there is no blowback damage to begin with.
If the source of the damage was an actual attack instead of an area of effect spell, then you could not opt to avoid dealing the damage, because there is no language indicating it is optional. It does not say "You can have the attacker take..." it just says when you use Spirit Shield to reduce damage from an attack, "the attacker takes an amount of force damage".