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

Yes. When Spectral Matron's trigger goes on the Chain, you choose Xin Zhao from your trash at that moment (targets are locked at finalization, Rule 352.4.b; FAQ #3434). The opponent can then play Disposal Order with Reaction targeting that same Xin Zhao.

Disposal Order resolves first (LIFO), recycling Xin Zhao to the bottom of your deck. When Matron's trigger resolves, its target is gone, so the instruction to play it is ignored — Xin Zhao is not played and no other card is chosen (Rule 359.3.e.7). This is the same interaction as Fizz + Disposal Order. If the opponent does nothing, the trigger resolves and Xin Zhao is played normally.