As a conservative, it's tough to avoid seeing opposing points of view. You'd have to avoid all late night shows, nearly all TV stations and newspapers, and most social media. We're quite accustomed to seeing opposing views and if it actually bothered us seeing them, we'd be frustrated virtually all the time.
Left-leaning people can quite easily participate in society without seeing opposing views. You can openly discuss even political activism at work without issue. Avoid Fox News and Breitbart and you're unlikely to see anything much different than what you already believe.
Maybe "offended" isn't the right word, but I do think it's a contributing factor.