I agree with you that musically, "Imagine" is a good tune.
As a formally trained and formerly professional musician, I (like you) tend not to care much about lyrics, or even notice them.
Nevertheless, I have always found the lyrics to "Imagine" to be particularly obnoxious. Maybe it's because in 1970 when that tune came out, I was a sophomore in college and had only just discovered conservatism (initially through reading Ayn Rand).
So given my then newly discovered passion for conservative political philosophy -- especially in the face of the suddenly ubiquitous New Left (and SDS in particular) -- I did listen to Lennon's lyrics, and found them disgustingly offensive and hypocritical. They offended my life-long love of America, my growing dedication to the principles of liberty and free markets, and my outrage at watching my peers (and professors) run around praising Che Guevera and quoting endlessly from Mao Zedong's "Little Red Book."
So my loathing of the "Imagine" lyrics has always over-shadowed my appreciation for the underlying melody and chord changes.
They like it just that way. Well-packaged propaganda.