There’s lots of suitable plastic materials, like I said I started with sheet PVC but now am using a recycled polyethylene product. There are “foamed” PVC sheets in thicknesses up to at least 1/4". Some of the guys here who use routers to cut outlines had sourced some thicker solid plastics, they probably got it from sign companies or suppliers to sign companies. If you use a roller collar there’s no worries with heat from friction. Templates have to be designed special for this use, obviously.
One of my favorite Greg Loehr quotes: “routers are for people who don’t know how to use jigsaws”. Don’t anybody take offense lol, years ago I said on here that there’s lots of good ways to cut outlines - everything from handsaws to worm drives and routers will get you there. After I wore out the first set of gears in my Milwaukee jigsaw, the guy who works on my tools asked me how “far” I’d cut with the thing. We did the math and came up about 26 miles (~14’ per board x 10,000 boards). I’ve almost worn out another set of gears since then. I’m retiring when they’re gone lol.
Slight edit to something I said a few posts back - when I cut with razor knife, it’s really more like heavily scoring the material. No need to cut all the way through, once it’s scored you just bend the piece and it will release along the scored line. Scoring a nice fair line takes some practice, but it can be done. You just want to make sure you never wander inside your line. Anything on the outside can be faired off, but if you go inside it’s back to the drawing board.