Born in Mainz, Neidlinger studied at the Frankfurt conservatory, where he was trained by Otto Rottsieper.
In 1950, he joined the Stuttgart Staatsoper, where he became very popular and was, in 1977, named an honorary member.
He also sang at the Paris Opéra (1953–67) and at Covent Garden in London in tandem with the Stuttgart ensemble (1955, 1963 (Telramund), and 1965 (Alberich)).
Neidlinger's portrayal of the villainous Alberich in Der Ring des Nibelungen was recorded in Georg Solti's Decca studio recording (1958–1965), and Karl Böhm's 1967 performance taped live at the Bayreuth Festival.
He sang at Bayreuth from 1952 to 1975, mainly Alberich, but also Klingsor in Parsifal, Kurwenal in Tristan und Isolde, Fritz Kothner in Die Meistersinger von Nürnberg, and occasionally Hans Sachs and Friedrich von Telramund.