What happens when two enchantments with 'when this enchantment enters the battlefield' both enter at the same time?

When two enchantments enter the battlefield at the same time, any 'when this enchantment enters the battlefield' triggered abilities on each of them will trigger simultaneously. They are not lost — all triggers that meet their conditions are placed onto the stack (CR 603.2).

Once all triggers have been generated, they are placed on the stack in 'Active Player, Non-Active Player' (APNAP) order: the active player (whose turn it is) puts their triggers on the stack first, then the non-active player does. If one player controls both enchantments, that player chooses the order their triggers are placed on the stack (CR 603.3b). The last trigger placed goes on the stack on top, so it resolves first.

Importantly, neither trigger 'sees' the results of the other resolving — they both triggered at the same time and with the same game state. Each trigger resolves independently once it reaches the top of the stack, with players receiving priority between each resolution (CR 608.1).

Example: It is your turn and you simultaneously put Seal of Cleansing and Omen of the Sea onto the battlefield (e.g., via a mass-cheat effect). Both 'enters the battlefield' triggers fire at once. Since it's your turn, you stack them in whatever order you prefer. You might let Seal of Cleansing's trigger go on the stack first, then Omen of the Sea's on top — meaning Omen resolves first (you scry/draw), then Seal's trigger resolves after.

This process is governed by the simultaneous-trigger rules (CR 603.3, 603.3b) and the rule that all abilities that trigger off the same event are placed on the stack together after the event completes (CR 603.2).