this is where national forest maps (if your in an area that they cover) come in handy. I was hunting an area in Thunder Basin National Grassland a few years back. I came to a gate just like you described. BLM on 1 side, and Private land on the other. 99% of the vehicles stopped at the gate. BLM maps showed the bLM lands, the road, and private on the other side. But the national forest map clearly showed that the road was a Public Access road and was highlighted as such. It was public access to a larger chunk of BLM on the other side of the private land. So we crossed the gate, traveled the access road to the public chunk, and had a great antelope hunt. We watched many other trucks stop at that gate and turn around. It is good to know the laws!
If your area is not in a Forest service area in which they have a map for it, call your local game warden and they may be able to help.
and.............always close those gates or you will anger many people/locals............not a smart idea!