Does Pa simply change his ideas or does he change in some deeper way in "Split Cherry Tree" by Jesse Stuart?

While Pa changes his opinion of Professor Herbert and his ideas about germs, he certainly undergoes change in deeper ways.

When Dave returns home late, his father interrogates him and learns that his teacher has made Dave stay after school in order to work off a fine incurred because he and others broke limbs on a cherry tree. Pa's initial anger is directed toward Dave; then, it takes on the clannish mentality of many who live isolated lives in remote areas after he learns that Dave is the sole student who has had to stay: 

"Poor man's son, huh...I'll attend to that myself in th' mornin'. I 'll take keer o' 'im. He ain't from this county nohow....
I'll straighten this thing out myself!....A bullet will go in a professor same as it will any man. It will go in a rich man same as it will a poor man."

And so, it is with rancorous and antagonistic feelings that Pa, who carries a gun with him, goes to the school the next day with Dave. Fortunately, Professor Herbert is a sanguine and cerebral man who has learned about the local culture. Although terribly alarmed at the sight of the gun and Pa's hostile words, he addresses Pa civilly,

"I was only doing my duty, Mr. Sexton...and following the course of study the state provided us with."

Having explained the circumstances pertinent to the cherry tree, he then takes Luster Sexton into a room and shows him the black snake that is to be dissected. Ironically, Pa teaches him about the value of this breed of snake, so the teacher agrees to find another snake for the experiments. Then, Prof. Herbert demonstrates how to see germs through a microscope and talks further with Pa until Dave's father comes to respect him. 

Pa also reaches the important realization that Professor Herbert has, indeed, been fair to Dave and he should not have been antagonistic to the teacher. Also, he proudly tells the teacher that, although Herbert has offered to cancel the debt, his people never take "somethin' for nothin'." Thus, he stays with Dave and helps him work off his fine.
As Luster Sexton helps Dave sweep, he demonstrates a powerful change that has taken place in his psyche as he tells Dave,

"I'm a dead leaf.....You must go on to school. I am as strong a man as ever come out'n th'hills fer my years and th' hard work I've done. But I'm behind, Dave. I'm a little man...."

Therefore, in addition to altering his ideas about Professor Herbert and schooling, Luster Sexton demonstrates that he is a complex and many-sided man--no country bumpkin, after all. He has clearly shown that he has the capacity to learn and to change his attitudes.