I play spectral matron and choose to play Xin Zhao from my trash. Can oppont play disposal order to prevent this?

Yes. Disposal Order can be played in response to Spectral Matron's "When you play me" trigger, and it will stop Xin Zhao from being played.

Spectral Matron's ability targets a unit in your trash when the trigger is placed on the Chain (Rule 352.4.b; FAQ #5659). Disposal Order has Reaction, so your opponent can play it while the Chain is Closed, targeting Xin Zhao and recycling it. Disposal Order resolves first (LIFO); when Matron's trigger then resolves, its target is gone, so the instruction to play it is ignored and no unit is played at all (Rule 359.3.e.7; FAQ #11060).

One caveat: you still could decline the "may" on resolution, but you can't swap to a different card — the target was locked in when the trigger went on the Chain.