That's not the point of the phrase, and even I think it's a bit tired by now.

The phrase asks the speaker to reevaluate their unspoken assumptions. I think 'lighten up and accept that the world is shitty' is a reactionary mode of thought, as if the 'real world' is a vast, static, unassailable entity and not an ever-changing tapestry of human activity. It is not a reasoned argument, it is not a response in a conversation, it is a demand that people shut the fuck up because the things they care about aren't worth caring about.

"check your privilege" is a diplomatic and concise way of saying 'you have no fucking idea what you're talking about, and yet you feel entitled to control the conversation; maybe stop doing that?'.