The rules say that triggers priority works like this:
Triggers Priority When multiple cards from different places trigger their effects at the same time, the priority order - unless said otherwise - is: Creatures (from first position to last) → Supports (from oldest to newest) → Hand (from oldest to newest) → Graveyard (from oldest to newest) → Exile (from oldest to newest).
Authority of the Consuls says: When a creature your opponent controls enters the battlefield, that creature is Disabled until the end of your next turn and you gain 1 life.
Authority of the Consuls doesn't explicitly increase it's priority to trigger before creatures.
When a creature your opponent controls enters the battlefield and that creature also triggers off of itself entering the battlefield then because they're both triggering off of the exact same event and therefore triggering at the same time then according to the priority rules the creature should trigger first because creatures trigger before supports.
That's not what is currently happening. Right now Authority of the Consuls is triggering first and disabling creatures before they trigger which then prevents their enter the battlefield ability from triggering at all.
Something isn't right. If this card is working as intended then it needs additional text to increase it's trigger priority to be before creatures. If the wording is correct then it's not following the rules and should be allowing the creature to trigger first.