For Ji-li, her red scarf isn't just a fashion accessory, it's a symbol of her cultural heritage and past. Check out how she describes it:
We were proud of our precious red scarves, which, like the national flag, were dyed red with the blood of our revolutionary martyrs. We had often been sorry that we were too young to have fought with Chairman Mao against the Japanese invaders, who tried to conquer China. (2.44)
The red scarf isn't just a symbol for Ji-li, it's a symbol for pretty much everyone. She thinks of the scarf as her connection to brave soldiers who fought for the cause before she was even born. It's a way of showing off her patriotism and support for Mao, like waving an American flag, only around her neck. In glorifying the fight for communism in this way, Mao subtly keeps people on his side, invested in a tale of glory instead of questioning his methods and new rules.
Ji-li's red scarf is her connection to stuff that happened way back when, before she was even born. She's proud of her heritage and wears that red scarf with pride. After all, it shows off to everybody just how revolutionary she is.
We can't help but think of something else here, though: Red reminds us of blood and violence, while scarves remind us of, um, things around necks. Under Mao's rule, people are silenced and subjected to violence. So what seems like a symbol for revolutionary awesomeness might also be seen as a symbol for just how hard life under Mao could be, too.