Turntable Mats: Rubber, Felt or Cork.

There are acrylic mats for sure, not sure if any thing made that is same composition as a modern vinyl record though.
Bar another vinyl record of course.

Delrin if you’re obsessed with matching to vinyl.  TTW used to make them. Colby Lamb can make them. And if you read other posts, what could match the hardness of a vinyl LP better than another LP? At least two others have mentioned that.

VPI’s used to make platters with a top layer of Delrin. The Aries 1, TNT-3, and TNT-4 had 3/8" of Delrin over 7/8" lead-lined aluminum, the TNT-5 7/8" Delrin over 5/8" stainless steel.

I’m using a Herbie’s Way Excellent Mat on my Rega P8. It’s thin, doesn’t rob the sound, looks great, and couples well with LPs. It’s fairly cheap ($59.99) and is actually made near my home in South Texas. I find it much better than the OEM Felt or cork mats. One plus is I don’t get a lot of static electricity from it and it doesn’t stick to records when changing or flipping sides.

https://herbiesaudiolab.com/products/way-excellent-ii-turntable-mat?variant=12654105919543

It has one feature that seems troublesome but turns out isn’t. Dirt from the LP sticks to the mat surface. My records are clean... but the mat will attract dirt you didn’t know was there.

To clean it I use tape. Sometimes a loop around my fingers that I dab on visible dust and about once a month I cover the entire mat with clear shipping tape. It’s overlapped strip over strip so all the tape comes off in one piece and any dirt stuck to the mat is picked up and trapped in the tape.

So atmasphere, the obvious question for us non-scientists.  What material(s) have the same, or very similar, hardness as a typical vinyl LP?

I'm not a fan of acrylic, but it can be made to have a similar hardness as vinyl. An LP would do nicely but does not have damping ability owing to its mass. I've thought a great deal about building a mat that has an aluminum or stainless substrate imbedded in the vinyl, as a means of stiffening it and making the whole thing more dead.