If you're confused by these two signs, I was too. I happened to see a couple of High Bridge DPW workers and pointed out the contradiction. They responded by saying that hunting legally requires a local permit (unclear by my reading). So, the righthand sign should read something like, "All persons are required to have a Borough of High Bridge permit to hunt on this property."
The bottom line for mtb'ers is that hunting IS permitted at the Nassau Trail with a proper hunting permit. I can't recall the exact start date for the hunting season there (also omitted from the placard), but as I recall it is right around next weekend...