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A decision to just follow orders is still a decision, but in this case OP wrote "local police recommended the signs to protect the business." If the manager follows their advice, they can come save the manager.

SIGFan43 wrote:My quandry is this: If I’m walking near the building in question, and I hear gunfire within, I’m likely to stay outside and observe through a window, because I might not risk my life to protect the manager if she is being attacked. My logic is that I might be charged with trespassing if I intervene while carrying concealed, regardless of what is happening indoors. Is my thinking flawed?

I wouldn't worry about being charged with trespassing if I entered after the incident started. Somebody already mentioned the necessity defense but even without that, the threat of a modest fine would not stop me from doing what I thought was morally right.

On the other hand, if the manager posted the signs, I would not come to their aid. I would respect their decision and let them suffer any consequences of that decision.