Depends on the attitude the other person shows towards myself, regardless if I am playing an Indie or an Official one.
If I as an Indie, offer my help to the officials and they reply in a reasonable/friendly way I will most likely behave like they want me to behave (not jumping into a fight; Helping them in a fight; Stopping a smuggler; Not stopping it;...). But if they just ignore me or try to give me useless orders, just to get rid of me I will pretty much do the same and ignore them.
If I as an Official Faction member encounter an Indie and he behaves in a good way that doesnt harm any others fun I will treat him pretty much like one of my own people and help him in every way possible. But if he decides to be a total moron I will most likely ignore him.
So, treat others like you would want them to treat you and nobody should have problems.