For example, if Merciless Executioner enters the battlefield, and both players have multiple creatures, which player chooses a creature to sacrifice first? Obviously the latter will have an advantage. Technically it can't be done simultaneously, so who should go first?
When multiple players must make a choice simultaneously, they do so in "Active Player, Non Active Player" order. This means that first, the player currently taking their turn chooses, then each other player chooses in turn order.
Rule 101.4 says
If multiple players would make choices and/or take actions at the same time, the active player (the player whose turn it is) makes any choices required, then the next player in turn order (usually the player seated to the active player's left) makes any choices required, followed by the remaining nonactive players in turn order. Then the actions happen simultaneously. This rule is often referred to as the "Active Player, Nonactive Player (APNAP) order" rule.