Neil, the "Southern Cross" is a constellation visible only in the southern hemisphere. Like the North Star in the northern hemisphere, it is helpful for navigation. The only correct term I know for the symbol under discussion is "Confederate Battle Flag," with "Confederate Flag" generally understood to mean the same thing.

The incorporation of the CBF into the Mississipi State Flag may have been in the nineteenth century, but I think it's fair to say the motivation had a lot to do with making a statement about white supremacy. While some may attach no such meaning to the CBF, the history of its post-Civil War use is such that it will never be divorced from that meaning. (Some people attach no derogatory meaning to the word "nigger," but likewise it will never be divorced from attitudes of hateful derision.) I think it's an inappropriate symbol for a modern state flag.

No American alive possessed black slaves, but virtually all white Americans enjoy some degree of prosperity and privilege that is generally denied to black Americans. There was no need for a NAAWP because the entire fabric of society, government, and the economy advanced the interests of white people while largely ignoring those of colored people. Likewise, there was no need for a "Miss White America" pageant because whites were always eligible for the "Miss America" pageant. Protests that "I didn't do it" ignore the fact that you benefited from it.