If Vex Apathetic is at a battlefield, and opponent reveals Tideturner, are they able to switch places with another unit or is the effect cancelled out from Vex?

Whether or not the Tideturner successfully swaps depends entirely on who is the Turn Player (the player whose turn it is currently).

According to RiftJudge FAQ #10318 and #10611, both Vex, Apathetic's ability and Tideturner's "When you play me" ability are triggered abilities that occur simultaneously when Tideturner is revealed and played. Per Rule 303.2.a, turn order dictates the resolution sequence via the Last-In, First-Out (LIFO) rule for the chain.

The Scenarios

1. If the Turn Player plays Tideturner:

1. Chain Placement: The Turn Player's Tideturner trigger is placed on the chain first. The Non-Turn Player's Vex, Apathetic trigger is placed on top.
2. Resolution: Vex's trigger resolves first. Tideturner becomes [Stunned] and gains the restriction that it cannot move for the remainder of the turn.
3. Outcome: When Tideturner's trigger attempts to resolve, the swap fails because Tideturner is restricted from moving.

2. If the Non-Turn Player plays Tideturner:

1. Chain Placement: The Turn Player's Vex, Apathetic trigger is placed on the chain first. The Non-Turn Player's Tideturner trigger is placed on top.
2. Resolution: Tideturner's trigger resolves first. The swap completes successfully.
3. Outcome: After the swap is complete, Vex's trigger resolves, stunning Tideturner at its new location.

Summary

• If you are the Turn Player: The effect is effectively cancelled (the swap fails) because Vex stuns you before the move can occur.
• If you are the Non-Turn Player: The swap will successfully execute before Vex stuns your Tideturner.

This interpretation is based on the interaction between triggered abilities, turn order (Rule 303.2.a), and RiftJudge FAQ #10318.