Construct the razor wire with the soviet command tent or construction truck. Approach the razor wire and jump shortly before colliding with it, the character will jump on top of the razor wire and can then run straight over it. I tested this at entre deux base at several locations on fairly level terrain as well as on an official server Conflict Full - 13585674 (US-MI).

This is specifically an issue with the razor wire that is able to be constructed by the soviets, the US razor wire that looks like it has metal X frames inside the wire does not appear to have this issue. Other razor wire variants may also suffer from this issue but I havent tested them. If you are too close or moving too slowly the soviet razor wire works as intended impeding movement and not allowing the character to climb over the obstacle.