If Vex is on the bf, can an opposing Tide Turner activate its effect?

Yes, Tideturner can be played and its trigger will go on the chain — Vex doesn't prevent the unit from being played, only stuns it after. Whether the swap succeeds depends on who the Turn Player is.

Both Vex's stun trigger and Tideturner's swap trigger happen simultaneously when Tideturner is played. Per Rule 383.3.d.1, the Turn Player places their triggers first, then the Non-Turn Player places theirs on top (LIFO).

• If the Tideturner player is the Turn Player: Vex's trigger resolves first. Tideturner becomes Stunned and can't move this turn. When Tideturner's own trigger resolves, the swap fails for Tideturner — though per partial resolution rules (Rule 359.3.e.11), the other targeted unit can still move to Tideturner's original location.

• If the Tideturner player is the Non-Turn Player: Tideturner's swap resolves first and completes successfully. Then Vex's trigger resolves, stunning Tideturner at its new location.

So the effect can activate in both cases — but the swap succeeds only when the Tideturner player is the Non-Turn Player.