So I'm going to assume the reason you're asking this question is to make sure you don't violate the "no exiting on reverse highspeeds" rule.
Here's the trick, while everyone thinks that's a rule, it's not actually a rule.
To answer the direct question, here is the definition of a "high speed exit" from the Pilot Controller glossary:
HIGH SPEED TAXIWAY− A long radius taxiway
designed and provided with lighting or marking to
define the path of aircraft, traveling at high speed (up
to 60 knots), from the runway center to a point on the
center of a taxiway. Also referred to as long radius
exit or turn-off taxiway. The high speed taxiway is
designed to expedite aircraft turning off the runway
after landing, thus reducing runway occupancy time.
I'd say you could argue it either way regarding that taxiway exit. My opinion is in a fast jet I most likely would roll to Delta, in a prop I'd exit Charlie with the determining factor being "which one gets me off the runway quicker". In the jet having to slow down to 10 on the runway to make that turn onto C is slower then rolling at 40 to D. In a prop I'm already doing 10 so the turn onto C is no big deal.
Now with regards to why it's not a rule.
From AIM 4-3-20 A
Exit the runway without delay at the first
available taxiway or on a taxiway as instructed by
ATC. Pilots must not exit the landing runway onto
another runway unless authorized by ATC. At
airports with an operating control tower, pilots should
not stop or reverse course on the runway without first
obtaining ATC approval.
You'll find nothing saying you can't exit onto a reverse high speed. So exit at Charlie with no worries.
However, another way to look at it is that some high speeds won't have a " taxiway centerline" for a reverse exit. I'd most likely avoid exiting if there is no centerline guiding me to the taxiway. I can't say it's against regs through.
At OXR both C and D have "reverse" taxiway centerline markings. For an example of an exit that doesn't, look at A5 off of 25L at KLAS.