"The Adventures of Huckleberry Finn" by Mark Twain repeats the word "ni**er" over 200 times. This fiction was required reading for me in their government ("public") school system. Why?

It's not taught now, for that reason.

But Twain was very much not a racist. The racism of his characters that use the word is meant to be judged by the reader, and is starkly displayed.

“It warn't the grounding - that didn't keep us back but a little. We We blowed out a cylinder-head.”
“Good gracious! anybody hurt?”
“No'm. Killed a ni**er.”
“Well, it's lucky; because sometimes people do get hurt.”

The author is displaying a callous racism in the characters. You could discuss it at a high school level, but you need to be very careful to avoid offence when discussing the book.

This same institution will fire a teacher for having a Holy Bible on his desk,

Not exactly. For insubordination of refusing, in writing, to remove other religious books from the top of the desk while teaching the class.

The Ohio Supreme Court concluded that Freshwater had the right to keep a Bible on his desk, ruling it was so inconspicuous that “Many students never even noticed the Bible or only realized it was in the classroom after it became a highlight of this controversy.”

But the state court ruled that Freshwater’s refusal to remove other religious materials — such as the books he had checked out of the library — demonstrated “blatant insubordination. That insubordination is established by clear and convincing evidence, and the record fully supports the board’s decision to terminate him on these grounds.”

• https://www.dispatch.com/story/lifestyle/faith/2014/10/06/u-s-supreme-court-affirms/23954840007/

which preaches God's love for all.

Not exactly. For instance Psalm 137:9 "Happy shall they be who take your little ones and dash them against the rock!"