I'm not a lawyer so I may be off base, but I would think at the very least you could be arrested for trespass if you violate such a sign. There may be other offenses but I'm not going to spend time digging for them.
Either way, I note that *many* of the more activist folks in the OC community hold similar views as you do, but *none* have volunteered to be the test case. Seems like it is easy to hold that stance behind a keyboard, but it is something else altogether to actually walk through that door and past that "sign that has no force of law".
Feel free to do so if that is your conviction, I eagerly await the video of the encounter. At this point in my life I, on the other hand, tend to handle such things so that the consequences are decided in my favor.
Moving on (until you post a video of such an event)