Do essentialist teachers give up teaching the basics if the students are not interested?

No. First of all there is no "essentialist " teachers. The curriculum taught by teachers is set by the state department of education the federal department of education, and the school district the teacher has very little say in the curriculum . The teacher is given a framework for each subject in each grade and told what to teach. When lesson plans are done the teacher must include the framework number, and objective for teaching the lessons. Textbooks are written to conform to the framework and state testing determine what is learned. It doesn't matter if the students are motivated to learn the subjects or not. Students come to school with various concerns and from various conditions. The Word learn is a verb which means the students have to take an active part in the learning process.