'If one of those who do not believe bids you to a feast, and you are disposed to go. whatever is set before you, eat, asking no question for conscience' sake.'
The same principle applies when they are invited to go to a pagan friend's house or banquet. There is no reason not to go if they wish to. Nor do they have to start asking questions about the meat. If its source is unknown they do not have to ask about it. Their conscience need not be so bound. They can eat whatever is set before them, accepting it as from the Lord and His fullness, and giving thanks to Him.
So the principle that he is stressing is that it is not whether the meat has been sacrificed to idols that matters. That affects things neither one way or the other. What really matters is when it is publicly known that it is so. Then it does matter because of the testimony it gives, and the effect that it might have on those who are spiritually weak. It is all a matter of testimony and concern for the thoughts of the weaker brother, not of the meat itself.