If you look at the Linn forum, PP, you will see they debate the sound of different plinth woods.
For Regas, several people sell metal subplatters to replace the plastic ones.
Pro-Ject use acrylic quite a lot, but I believe the platters are MDF on the budget models (or am I thinking of the Rega RP1?).
Michell use a acrylic/vinyl mix for their platters, claiming it matches a record's 'impedance'. Seems fairly plausible to me, though cannot say I understand the science.
Given that many musical instruments are made of wood, and none (I think!?) is made of acrylic, I think perhaps acrylic is more inert and therefore lends itself to production of a neutral sounding item. I think the WHF fave, the Clearaudio Innovation, is made of both wood and acrylic, so maybe that is an ideal solution?