Can Someone Explain Identity Politics in the USA?

I'm sorry, but being a non Westerner, I'm failing to understand what is called Identity politics, is it only me and non Westerners or there are Americans and Western Europeans who are also not getting it?

To avoid any controversies in the main post, I'm using this meme:

If someone can identify as another gender, race, age, ethnicity, what stops the world from faking its whole existence? Everything can identify as something else, even the opposite and let's make life more miserable and complicated than it already is.

Anybody, help?!