Can I play a reaction if I have Vex apathetic on a battlefield and my opponent plays units. Like react to the stun?

Yes, you can play a Reaction after Vex, Apathetic's trigger is on the chain.

Here's the timing breakdown:

1. Your opponent plays a unit. As a permanent, it leaves the chain immediately — no response window to the unit being played (FAQ #7795, #5909).
2. The unit enters the board. Vex, Apathetic's triggered ability condition is met and it goes on the chain as a Pending item.
3. Now the game is in a Closed State with a pending trigger. During the Execute step of FEPR, players get priority to play Reaction cards or abilities (Rule 813).

So you cannot react before Vex's trigger resolves — there's no window between the unit hitting the board and the trigger firing. But once Vex's trigger is on the chain, you can respond by playing a Reaction spell or activating a Reaction ability (e.g., Flash to save your unit, a pump spell, or anything else with Reaction timing).

Just keep in mind: Vex's stun does not target — it uses programmatic selection (FAQ #9312, Rule 355.10.d). So "can't be targeted" protections won't prevent it, but you can still respond to the trigger itself before it resolves.