Zeitgeist has been in widespread use for a long time (at least a century and a half),2 so it no longer needs to be capitalized or italicized.
His desire to get under the skin of the establishment caught the zeitgeist, and to the young of the time he proved a striking standard-bearer for disaffection and change. [The Music Magazine]
The year 1964 was one of those moments when the reigning “ism” — abstract expressionism — had sputtered out, and the zeitgeist screamed for change. [Star Tribune]