It’s pronounced Pal-uh-steen in Texas and reportedly is named after Palestine, Illinois. The Wikipedia entry for the Illinois city does not give a pronunciation.
The Texas town is county seat for Anderson County. The estimated population for 2019 was 17,730. The city is 65 percent white and 25 percent black. For every 100 women 18 and over, there are 78 men. About 21 percent of the population lives below the federal poverty line.
Palestine was named by Daniel Parker, who lived and preached in Virginia, Tennessee, Indiana and Illinois before moving to Texas in 1834. Parker and many other Baptists objected to the establishment of a national Baptist organization, saying such organization “violated the right or government of the Church of Christ in forming themselves into a body and acting without of the union." Parker is considered one of the more important frontier preachers in Texas.
He was a brother of John Parker and an uncle of Cynthia Ann Parker, who was kidnapped by Comanche raiders at Fort Parker in Limestone County on May 19, 1836. Cynthia Ann later became the wife of Peta Necona and had three children by him, including Quanah Parker, the last war chief of the Comanche.