People did not flee to Canada during the Revolution to avoid fighting. It was after the Revolution, when their property was confiscated, that Loyalists went to Halifax, and from there, some went to London. What were they to do? They lost everything, and British soil was the only place they were welcome.
Don't confuse that with the Vietnam draft evaders. The circumstances were not even remotely alike.
People fled before, during and after the war, my family had members that chose to abandon America’s future promise and choose Canada during that time.
In general the American attitude was good riddance to our losers.