I was there a few weeks ago. High clearance and 4WD are mandatory to get all the way to the Chukar Trail head. And don't go too heavy; the hike in is a bit of a bear while lugging a small cat frame! :
I don't know about "mandatory." Unless things have changed or if the road is really wet, a 2WD vehicle will get you there. I made it with no problem in my 2WD Chevy S-10 a couple years ago. It had some clearance but nothing that the factory didn't install.
I agree with Jonny....
4WD isn't needed unless it is wet. If it is wet you're probably SOL even with 4WD. Clearence is all you need. Although I have even seen honda accords and the like down there. I imagine they scraped some though.