The press doesn’t matter, material wise. Rubber plunger is closest thing to contact the coffee, and it usually doesn’t. The other tube could be made of stainless steel, along with the honeycomb filter holder on bottom.

If that were a taste issue for some reason, it would way up the manufacturing price, but you can put a glass tube encased in stainless steel or plastic. It’s been done with thermos’ and water bottles.