No, but the Dead Three are still around
Several gods died during the Time of Troubles, notably including the Dead Three: Bane, god of tyranny, Bhaal, god of murder, and Myrkul, god of death. However, gods are difficult to destroy in the Forgotten Realms, and all three of the dead gods have devised schemes to return to power. Bane’s plot was successful, and he has supplanted the Godson who inherited his portfolio. Bhaal’s scheme was the main plot of the Baldur’s Gate video games. Myrkul appeared in the Neverwinter Nights video games, but so far he still appears to be a dead god, rather than a god of death.
Therefore, the entries for Bhaal and Myrkul currently appear to be there primarily for historical interest, for DMs who want to use them in the past of the Realms, or who want to feature their schemes to return to power. They do not indicate that Kelemvor has lost or changed his portfolio – yet.
Some are listed in the Tal'Dorei Campaign Setting (though they may be slightly different from those used in play)
As you guessed, some of the house rules used in Critical Role do indeed appear in the Tal'Dorei Campaign Setting book. However, the book does not clearly distinguish which of the listed house rules or homebrew feats are actually house rules used in Critical Role, or whether the version of something in the book actually matches the version used in actual play during Critical Role.
Michael Liu's answer links to sources on /r/CriticalRole on reddit where some of the Critical Role houserules are listed. Of those, the following ones appear in the Tal'Dorei Campaign Setting as feats:
Matt Mercer allows his characters to drink potions as a bonus action.
This appears in the book in the form of the Rapid Drinker feat
(p. 109):
Through a lifestyle of hard, competitive drinking, you’ve learned how
to quaff drinks at an incredibly accelerated pace. You gain the
following benefits:
- You can drink a potion as a Bonus action, instead of as an action.
- You have advantage on any saving throws triggered by ingesting an
alcoholic or dangerous substance.
Mercer also allows characters to cast multiple spells per turn
(without changing their casting times), ignoring the 5e rules
limitation around bonus-action spells. This also appears as the
Spelldriver feat (p. 109):
Prerequisite: Character level 8th or higher
Through intense focus, training, and dedication, you’ve harnessed the
techniques of rapid spellcasting. You are no longer limited to only
one non-cantrip spell per turn. However, should you cast two or more
spells in a single turn, only one of them can be of 3rd level or
higher.
The Tal'Dorei Campaign Setting book also has an entire section in the same chapter (Chapter 3) on "Optional Campaign Rules and Guidelines". Within that chapter, it suggests that when running games with larger parties, the DM may want to give out the Rapid Drinker feat (or the equivalent primary benefit) and eventually give out the Spelldriver feat at 8th level. It also lists accelerated downtime mechanics and Matt Mercer's alternative resurrection rules. All of these seem to generally match the house rules listed in Matt Mercer's comment on /r/CriticalRole that Michael Liu's answer links to.
This section is accompanied by the following sidebar:
Optional Rules of Critical Role
For those who have watched along with our adventures, you may see some
of these optional rules as familiar. Many of the elements included in
this chapter are based on or retooled versions of the house rules we
tried within our own campaign. Some have undergone a number of changes
for balance as we try new things and learn from our experiences. For
those that are curious, the ones we utilized within our own game are
Rapid Quaffing and Multi-Spell.
As such, these optional rules may not perfectly match the CR houserules as used in actual play, but they are a refined version of those houserules.
Best Answer
The Explorer's Guide to Wildemount is official in that it is published by Wizards of the Coast, but none of its content is permitted in AL play. This announcement on the D&D AL website says:
Emphasis mine.
Everything below is in a sense obsolete, as there is no more PHB+1 rule, but the new structure for AL sources still does not permit EGtW.
Furthermore, the AL Player's Guide explicitly lists what sources are permitted by the "PHB+1" rule in the Forgotten Realms AL campaign:
The AL Oracle of War campaign (set in Eberron) has no “+1 Rule”; instead, it permits character options only from the PHB, Eberron: Rising from the Last War, and XGE. Character options from other sources, including the Explorer's Guide to Wildemount book, are not allowed.