Actually, i think it would be quite different. For one, churches in the States started going anti-masonic (acusing us of devil worship and the like) as a response to the Morgan Affair. Some went so far as to expel all masons from their congregations. I think Masonry as an organization would be more widely accepted as what we are if this event had not happened.
However, i do agree with you Bro. Rustybones
, most people in my Lodge don't know about the Morgan Affair. I learned about it on the History Channel myself. But, i think a lot of the anti-masonic sentiments around today are a direct result of this incident, even if the people who hold them don't know their origins.
The question is, how do we go about reversing these sentiments now?