This is a mess I can't sort out.
We may need a BY depending on common name, because CLT indicates the baritone may have more titles without the apostrophe, clashing with the actor.


Carlos Álvarez the baritone/performer/music related credits
(b. August 12, 1966)
Manually sorted works (in database):
• The 7 (The Oakley Seven) (likely invalid/no credit or another "Carlos Alvarez")
• Bellini: I Puritani
• Carmen
• Don Giovanni: W.A. Mozart: Opus Arte
• Invito all'Opera 25 - Macbeth: DTS
• Julio Iglesias: Starry Night
• La Forza del Destino
• Macbeth (only this profile found: UPC 809478009221)
• Monsters Of Metal (definitely another person - but is there a credit?)
• Puccini: Madama Butterfly: Original 1904 Version: Teatro Alla Scala
• Rigoletto (Verdi): Covent Garden, Downes
• Verdi: Giovanna d'Arco: Teatro alla Scala
• Verdi: Otello
• Verdi: Otello (Salzburg 2016)
• Verdi: Rigoletto (Barcelona 2004): Legendary Performances


Carlos Alvarez (common name) the actor
(BY unknown)
Manually sorted works (in database):
• For Greater Glory: The True Story of Cristiada
• Highway Patrolman (El patrullero)
• The Other Conquest (La otra conquista)
• Sniper

CLT results (regardless of either person):
Carlos Álvarez: (6 unconfirmed, 1 confirmed, 0 invalid)
Bellini: I Puritani
Don Giovanni: W.A. Mozart: Opus Arte
La Forza del Destino
For Greater Glory: The True Story of Cristiada verified by me
Macbeth
Puccini: Madama Butterfly: Original 1904 Version: Teatro Alla Scala
Verdi: Otello

Carlos Alvarez: (9 unconfirmed, 3 confirmed, 1 invalid)
The 7 (The Oakley Seven)
Carmen
Highway Patrolman (El patrullero) verified by me
The Hire [no credit] verified by me
Invito all'Opera 25 - Macbeth: DTS
Julio Iglesias: Starry Night
Monsters Of Metal
The Other Conquest (La otra conquista) verified by me
Rigoletto (Verdi): Covent Garden, Downes
Sniper verified by me
Verdi: Giovanna d'Arco: Teatro alla Scala
Verdi: Otello (Salzburg 2016)
Verdi: Rigoletto (Barcelona 2004): Legendary Performances

It seems I am getting close to the truth here.
I feel quite confident announcing common name for the baritone as Carlos Álvarez.
And common name for the actor as Carlos Alvarez.
With this in mind, a BY for the baritone wouldn't help much, since there is now a clash between "Carlos Alvarez"; the actor and member (guitarist) of the metal band Bludgeon.
For "the 3rd" Carlos Alvarez, I have found that he has a known BY, but that it's not needed, since his common name is Carlos José Alvarez, but he needs a crosslink for his credit in "The 7".


Carlos Álvarez the baritone/performer/music related credits
(b. August 12, 1966)
Manually sorted works (in database):
• Bellini: I Puritani
• Carmen
• Don Giovanni: W.A. Mozart: Opus Arte
• Invito all'Opera 25 - Macbeth: DTS
• Julio Iglesias: Starry Night
• La Forza del Destino
• Puccini: Madama Butterfly: Original 1904 Version: Teatro Alla Scala
• Rigoletto (Verdi): Covent Garden, Downes
• Verdi: Giovanna d'Arco: Teatro alla Scala
• Verdi: Otello (Salzburg 2016)
• Verdi: Rigoletto (Barcelona 2004): Legendary Performances


Carlos Alvarez the actor
(BY unknown)
Manually sorted works (in database):
• For Greater Glory: The True Story of Cristiada
• Highway Patrolman (El patrullero)
• The Other Conquest (La otra conquista)
• Sniper

CLT results (regardless of either person):
Carlos Álvarez: (3 unconfirmed, 6 confirmed, 0 invalid)
Bellini: I Puritani verified by me
Carmen verified by me
Don Giovanni: W.A. Mozart: Opus Arte
La Forza del Destino
For Greater Glory: The True Story of Cristiada verified by me
Macbeth verified by me
Puccini: Madama Butterfly: Original 1904 Version: Teatro Alla Scala
Verdi: Rigoletto (Barcelona 2004): Legendary Performances verified by me
Verdi: Otello verified by me

Carlos Alvarez: (5 unconfirmed, 3 confirmed, 5 invalid)
The 7 (The Oakley Seven)
Carmen verified by me
Highway Patrolman (El patrullero) verified by me
The Hire [no credit] verified by me
Invito all'Opera 25 - Macbeth: DTS verified by me
Julio Iglesias: Starry Night
Monsters Of Metal
The Other Conquest (La otra conquista) verified by me
Rigoletto (Verdi): Covent Garden, Downes
Sniper verified by me
Verdi: Giovanna d'Arco: Teatro alla Scala
Verdi: Otello (Salzburg 2016) verified by me
Verdi: Rigoletto (Barcelona 2004): Legendary Performances verified by me