How to make readers care so much when the stakes are so low - Trollope's fiction

Trollope's Barchester Towers is pretty much a case study in how to make the readers care so much when the stakes are so low. Would you ever think you could get engaged for a minute with a plot like this (let's see if I can lay out the bare outline): Slope, the insinuating churchman, advances in stature by aligning himself with Bishop Proudie's wife and being a strict believer in Sabbath observance; at the Bishop's request he goes to Harding, who used to be the Warden of the local poorhouse (a cushy and remunerative job) and offers Harding the job back; when the Bishop's wife interferes, though, he backs her in her plan to give the cushy job to another minister, Quiverful (!), who lives in poverty trying to raise his 14 (!) children. But things change: Slope breaks from Mrs. Proudie and decides he wants to marry Hardin's widowed daughter, so he goes back and promises the job to Harding, then goes to Quiverful and tells him to back off. When Q's wife brings the issue to the Bishop and Mrs. Proudie, it leads to a big confrontation - Mrs. P tells Slope to get lost, Slope tells the Bishop - about the most feckless man in literature - to bar his wife from interfering in church business. For the moment, the Bishop sticks w/ Slope (and Harding) - but we know this won't last, as Slope has made an enemy of the powerful Mrs. Proudie. Got it? And why should we care about 19th-century church politics? Well, we don't - but Trollope engages us with the characters, and with their ways of speaking and thinking. In other hands, this would be a novel about global politics or some topical domestic struggle, but Trollope seems to delight in making his novel entirely provincial and overcoming our resistance, engaging us even though we actually care very little about the outcome - just about the process.