It’s quite simple: when liberals get upset about things like businesses promoting bigotry and persecution, it’s because they’re easily-triggered snowflakes, but when conservatives get upset about things like Starbuck cups, people saying “Happy Holidays”, having to “press 1 for English”, American Sniper not winning the “Best Picture” Oscar or the president wearing a tan suit, it’s because those things are important.
The kind of person who supports Trump and uses terms like “cancel culture” and “social justice warrior” is most likely somebody who doesn’t really understand the political issues they talk about.