What is the default Empire Titles Restricted By Organized Faith game rule in CK3?

Disabled: Anyone can create Empire Titles with regular requirements. (patch 1.20.1.2)

Does changing the Empire Titles Restricted By Organized Faith rule disable achievements?

No: none of its 3 settings carries the flag blocks_achievements in patch 1.20.1.2.

Game rule · Titles & Realm · Tweaks

Empire Titles Restricted By Organized Faith

Enabled
Enabled, Headless Exempt
Disabled · default

Empire Titles Restricted By Organized Faith is a game rule in Crusader Kings III (Titles & Realm and Tweaks) with 3 settings: Enabled, Enabled, Headless Exempt and Disabled (the default). None of its settings disables achievements. Patch 1.20.1.2, from game/common/game_rules/01_empire_faith_gate_rules.txt.

This section as JSON: /raw/game-rules.json

Quick answers (2)

What is the default Empire Titles Restricted By Organized Faith game rule in CK3?: Disabled: Anyone can create Empire Titles with regular requirements. (patch 1.20.1.2)
Does changing the Empire Titles Restricted By Organized Faith rule disable achievements?: No: none of its 3 settings carries the flag blocks_achievements in patch 1.20.1.2.

3 settings

Enabled
Requires an Organized Faith and Head of Faith's approval to create Empire Titles. Affects Feudal, Clan, and Tribal Rulers.
The script checks it 2 times, in 2 places
Scripted triggers 2
- empire_creation_hof_requirements_trigger
- empire_faith_gate_enabled_trigger
Every has_game_rule = empire_faith_gate_on in game/common and game/events, by the top-level object it sits in.
empire_faith_gate_on
Enabled, Headless Exempt
Requires an Organized Faith and Head of Faith's approval to create Empire Titles, but Faiths without a Head of Faith are exempt from the approval requirement. Affects Feudal, Clan, and Tribal Rulers.
The script checks it 2 times, in 2 places
Buttons of the game's windows (scripted GUIs) 1
- empire_faith_gate_vassals_check
Scripted triggers 1
- empire_faith_gate_enabled_trigger
Every has_game_rule = empire_faith_gate_no_hof_exempt in game/common and game/events, by the top-level object it sits in.
empire_faith_gate_no_hof_exempt
Disabled
Default
Anyone can create Empire Titles with regular requirements.
empire_faith_gate_off

Source: game/common/game_rules/01_empire_faith_gate_rules.txt line 1 (key empire_faith_gate), modifiers from game/common/modifiers, names from the English localisation; Crusader Kings III 1.20.1.2.