If we’re striving to be inoffensive, shouldn’t we go all in?

So I was reading an article about this American country pop band, which recently changed their name to remove one of the words in their band name, which can be considered offensive and even racist.  The name of this band included a term used to refer to the American south, which started with a D, ended with an E, and is five letters long, and includes the letters I, X, and another I (not necessarily in that order).  It’s no longer a word that can be said (I think), so I can’t spell it out or say it.  So now, this band has a new two word name. 

As I read the article, it occurred to me that one of the other words in their band name can also be considered offensive.  In order to not offend, I won’t say it, or spell it out, but it is considered by many to be a derogatory term used to refer to women, and is also a term used to refer to baby chickens.  The word starts with a C, ends with an S, and is six letters long, including the letters, H, I, C, and K (not necessarily in that order).

My question is, if it is our society’s goal to eliminate offensive language from our vocabulary, wouldn’t this word also need to be removed from this band’s name?  After all, are not women owed the same respect as anyone else, and should not be referred to using a word considered by some to be derogatory?  This makes me wonder why this all female band chose to keep this women-specific derogatory word, while removing the widely considered racist word from their band name.  There is still one word left in their original band name which could be used, either on its own, or with some other non-offensive words.  And since they were already making a name change, why not just take care of the issue with both words at the same time?

They could have made an announcement declaring that they would no longer be known as The D_ _ _e C_ _ _ _s, but now would know as the The.  Or perhaps, they could have just gone with The Southern Women, since there is no current band known by that name.