Yes.
If they tell you to leave they may believe that you are committing trespass, loitering, disturbing the peace, or some other offense. Usually what happens is that they ask you to leave or suggest that you leave, carefully doig so in a way that they can say you agreed to leave voluntarily.
In order to compel you to leave against your will you would have to be committing some offense. I don't know if you are or not, but it doesn't sound like it. If you are told to leave you can ask if you are suspected of committing an offense. If they say no then you can decline. If they say yes then you might risk citation or arrest if you remain.
I highly doubt the police really care if you are there or not- they just want to resolve the problem in a manner that causes complaints to stop.
MM: First off, thank you for answering my question directly! I was 99% sure that the answer was yes after reading Wikipedia's "1st amendment to the constitution - Private Action". But it is very nice to have you confirm it! Thank you.
Yes, if the police asked me to leave, I would immediately ask them if I was breaking the law in any way. If they said yes, I would ask them how. If they seemed content to arrest me if I didn't leave, I would leave, to diffuse the situation for the time being. But I would come back the next day in a way whereby I was no longer breaking the law (ie: loitering/ trespass). However, while researching "picketing" and "freedom of speech", I did come across those topics and will look into them further before going there.
I do have 2 simple (most likely) questions, 1, regarding, ironically, what we both mentioned above, "trespass". The 2nd could be about either trespass, or more likely, if they wanted to say that I was trying to injure them from a monetary or reputation standpoint.
1) Let's say, standing on the public sidewalk, not committing any offense, is legal. But what if I were on that sidewalk and a group of people needed to walk past me and I stepped either onto the grass between the sidewalk and the curb, or, I stepped onto their private property, like the lawn in front of the restaurant that they care for. Even if I am just on there for 5-10 seconds, and let's say they videotaped me doing that, how likely is it that they would have a "valid basis" for filing a charge of trespass given that I am obviously not there for the purpose of being a "customer"? Truly, this concerns me 99% more than the police being called for general purposes related to me being there with my sign.
2) From a technically legal perspective, how much of a difference does it make if I am standing on the public sidewalk in front of their building versus standing next door on the public sidewalk of the next building over? Simply, would they have just as strong of a claim that I was "willfully and maliciously carrying on certain activities designed to injure management"? I'm 'assuming' that they wouldn't have a legitimate complaint for trespassing or loitering if I am not on their property (assuming they did when I was directly in front of their store, hypothetically speaking).
Again, thank you.