You see the issue here wasn't about Anderson's beliefs in slavery. That is a smoke screen. It was about the forts and the authority of the United States regarding South Carolina possible secession. You see you can still believe in Slavery and still also believe that the States didn't have the right to secede. And the Forts were viewed as being the key to forcing that State to remain in the Union. The key word here is "Force".
Yes, Anderson was chosen because of his southern background. Would South Carolina accepted that change in command so easily if a known abolishionish from Boston had been chosen to replace a popular garrison commander of several years service in that position?