Why would they fine you? As a deterrent to you and others. The fear is that someone will ignore the signs, injure himself and then sue, claiming something like "Cyclists ignore road closed signs all the time. In this case, there was a latent danger at the construction site so you should have put up a fence to protect me." The settlement is paid for with your tax dollars and then you complain about high taxes.
As suggested above, use discretion. I was touring across PA back in 2013. Ignored a bridge out/detour sign, hoping that the bridge would be crossable by bike, as they sometimes are. Got to the construction site as the crew was removing the final girder. The crew said I could walk across the stream once the girder had been cleared. That was nice of them because the detour was really circuitous and hilly. They were quite amazed when I took off my cycling shoes, put on my sandals and crossed the stream while keeping my fully-loaded bike out of the water. I almost felt like they were expecting me to fall into the water.
Had a similar experience years before during a group day ride. A bridge was totally gone. Detour would have added maybe 5 miles to an already hard ride. It had recently started raining, and we were right on the edge of our planned food/water stop. We all walked across the creek, which was actually warmer than the chilly rain falling.