Do bonuses to AC stack?

Question

The Warforged get +1 to AC from their Integrated Protection feature.

The forge domain cleric can use the feature Blessing of the Forge to enchant their armor for another +1 to AC.

The Soul of the Forge feature forge domain clerics get at 6th level adds another +1 to AC.

Fighters with the Defense fighting style get another +1 to AC.

Assuming the use of plate armor and a shield, is it possible to take 6 levels in forge domain cleric and one level in fighter with the defense fighting style to get 24 AC?

Answer 1

These stack.

Here are all the relevant features:

Blessing of the Forge

[...] At the end of a long rest, you can touch one nonmagical object that is a suit of armor or a simple or martial weapon. Until the end of your next long rest or until you die, the object becomes a magic item, granting a +1 bonus to AC if it’s armor [...]

Soul of the Forge

[...]

• While wearing heavy armor, you gain a +1 bonus to AC.

Defense

While you are wearing armor, you gain a +1 bonus to AC.

Integrated Protection

Your body has built-in defensive layers, which can be enhanced with armor:

• You gain a +1 bonus to Armor Class.

[...]

This adds up to +4 AC, and there is no reason for these not to work together, as they are all just bonuses to your AC, not methods of setting it. And finally, wearing plate armor for a base Armor Class of 18 and a shield for +2 AC brings us up to 18+2+4=24, as desired.

Answer 2

Bonuses in general stack in 5e

Unlike in Pathfinder or 3e, there is no rule in 5e that bonuses of the same type do not stack. By default bonuses always stack, as long as they are caused by features that have different names.

This exception to stacking is on p. 252 DMG, Combining Game Effects:

Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them - the most potent one - apply while the durations of the effects overlap. (...) Game features include spells, class features, feats, racial traits, monster abilities, and magic items. See the related rule in the "Combining Magical Effects" section of chapter 10 in the Player's Handbook.

And, mirroring that on p. 205, PHB, under Combining Magical Effects, for spells in particular:

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect — such as the highest bonus — from those castings applies while their durations overlap.

Because in your case all the features have different names (Integrated Protection, Defense, Blessing of the Forge, Soul of the Forge), they all stack. Together with the 18 base AC for full plate and +2 from Shield they will get the character to 24 AC.