Tassajara road can be driven up in any car, but you have to drive carefully. And watch for overheating of the engine. Drive it slow and steady and steer around the gullies and so on and you'll be fine, try to just drive up it as if it were paved, or using the wrong (too high) gear, and you might not be fine. If your engine starts to overheat, drop the gear to a lower one, the one you should have already been in that is, and slow down. If it won't drop temperature, stop and wait, then restart, and don't try driving it in a high gear and too fast. It's not unlike the road into the lost coast, except the lost coast in winter can't safely be done in any rear wheel drive vehicle.
I've driven up that in the worst beater, shot suspension, etc, and it made it, but you do have to drive with awareness. Given that the zen center is at the base of the climb, a bit of mindfulness should be in order anyway.