Sometimes, it's obvious, with dogwhistles like 'states rights', 'northern aggression', and the usage of the word 'negro' by white authors in books written past the year 1950. Other times, I've really enjoyed a book like Sherman's March by Burke Davis, but felt kind of icky after reading it without being sure why - an extreme emphasis on the civilian southerners' response to the March, Twain-esque slave dialogue (I believe he drops a 'massa' before page 100), and the author's other books being biographies on Stonewall Jackson, Robert E. Lee, and Jeb Stuart all combine to make a slightly unsavory picture, and make me second-guess parts of the book.
Are there clear alarm-bells to suggest that a work may not be objective, akin to the usage of the term Anglo-Saxon? How should a non-historian approach Civil War media?
I'm not a formally trained historian, so take what I say with a grain of salt.
One of the greatest factors when evaluating a work on the Civil War is what sources the author uses. Public figures such as Jefferson Davis wrote books after the war espousing and defending the Lost Cause ideology. A reliable author will focus on what a historical figure said *before* and *during* the War, rather than what they claimed *after* the War to justify their actions.
Another thing to pay attention to is how the author talks about freedmen and US Colored Troops. For example, in Shelby Foote's books, he always portrays African Americans talking in a corny vernacular, and presents them as jolly silly fellows. This is an enormous disservice to the massive numbers of enslaved people who underwent massive hardship before, during, and after the Civil War; and suggests that his work should not be taken seriously.
Also note how much emphasis a writer puts on context. James McPherson's excellent magnum opus on the Civil War, "The Battle Cry of Freedom," opens with two hundred pages of background explaining the causes of the Civil War in great detail. If an author is claiming to write a comprehensive history, but skims over or ignores the background of the War, take what they say with a grain of salt.
Finally, consider the author's tone when he discusses particular historical figures and events. Are Robert E. Lee, Jeb Stuart, and Stonewall Jackson presented as chivalrous heroes, or as real human beings? Does the author try to justify or ignore atrocities such as the Fort Pillow Massacre, the Battle of The Crater, or Andersonville?
Some books on the Lost Cause ideology and the historiography of the Civil War which I find particularly helpful:"The Myth of The Lost Cause and Civil War History" by Gary Gallagher"Causes Lost, Won, And Forgotten: How Hollywood And Popular Art Shape What We Know About The Civil War" by Gary Gallagher."