Some phono amps and the phono stage of some pre-amps invert the polarity of the signal from the pickup they are fed, others don’t. Some recordings contain music whose absolute polarity has been reversed in the recording process, others don’t. Some recordings contain music recorded such that one or more channels in a multi-track recording are in polarity opposite that of the other channels in the multi-track recording. It’s a real mess.
Also a mess are many loudspeakers, even very expensive ones. The three drivers in many 3-way speakers are wired in polarity opposite one or more of the other others(s). The Quad ESL inverts the signal, but the speaker as a whole is in polarity with itself. Since the polarity of some amplifying stages and many recordings is so random, what difference does it make? Sheffield direct-to-disc LP's are known to be in varying states of polarity.
The Dynaco Quadaptor of the 1970’s created a rear-channel signal that were merely a left-minus-right inversion of the front channels (the opposite of a left-plus-right mono signal), to reproduce the out-of-phase content found in some stereo recordings, particularly live recordings made in large venues.