We already implant subdermal RFID chips in animals and people. You just put the chip inside a non-biologically reactive substance and it's fine.
The bigger problem is scanning distance. You're limited to only a dozen meters or so if you're not using an active RFID with battery. ~100 meters with a battery but then you have to change the battery every now and then.
I’ve had a toll pass device for 10 years. It gets scanned at 80mph or more and hasn’t needed a new battery yet. The newest models are the size of a credit card.
Yeah, it goes through just about any material. I used to keep one under my seat on my motorcycle. So it would scan through me, the rubber/foam/whatever seat and into the metal box under my ass. That was 10+ years ago in the Orlando area, I can't imagine they have gotten less accurate