I think most see it as rich people arguing with rich people. Most just look at the 'top' players making millions of dollars a year to live out their childhood dream and can't comprehend how they could complain and strike in that situation. To be honest - that's true. Even the minimum contract players make more in a year than most do in 10-15 years at their careers, so it's hard for the general public to relate and sympathize with them.
Of course the reality is the Owners typically all make hand over fist also - but their numbers aren't truly public (and if they are, it's all skewed and doesn't really reflect the profit they made) and the general public just doesn't relate to them like they do the players.
I don't think that makes people stupid - perhaps just a little short sighted.
The exploitation of minor league players is REALLY something the general public could relate to and support. That's something that really pisses me off and I wish there was a way to fix that. And of course, as a fan, I'd love to see a world where neither the owners or the players become become quite as rich so they could lower the price to attend games so the average joe and his family could attend more often.