I don't think "most" Americans would see a scab (person crossing a picket line to work and/or a person in a union shop not paying dues) as a "heroic" figure. They might sympathize with them for doing what's necessary (in their eyes) to put food on the table.
My dad recently told me that when I was a wee lil' Piedmont that the USW tried to organize the copper foundry he worked at in the early 1990's and they actually went on strike.. but he kept working because he couldn't afford not to.
It depends on how your feel about unions, if you've ever worked in one, how the union treated the workers and what happened when you retired.
Most people that haven't worked in a place that had a strong one say "they only protect the losers, the lazy and the ones that need fired". Ive seen that but being Southern Baptist or trusting in God to protect your job really isn't the issue. It's how you feel about union objectives, activism, and if you agree with all that.
Inside the union, except recently due to the IBTs campaign against the members, most of us get negative attitudes due to the local BA, if they don't trust he's on their side. Those who like their BA are more likely to support the union in other ways.
WE are the union. We need to stand up for each other regardless of what the locals or IBT does. When nonmembers see our strength they are more apt to join.
Some won't support because the Teamsters support politicians that support issues like abortion and/or homosexuality and that is against their Christian beliefs. Everyone needs to make their own decision.