Today's methods of changing speed do it without a pitch shift, so may be less obvious.
It wasn't obvious to most people, just as an SSB received signal can be slightly off "zero beat" without sounding strange.
Strangely, some people seem more sensitive to phase errors between stereo channels, than absolute frequency.
I'm not at all sure how that works, but it seems to be those that listen in very quiet surroundings, or with headphones.
The ABCFM transmitter at Mawson, Western Australia was (I'm not sure, if it is now) fed with the discrete L&R signals, via a combination of microwave bearers & landlines.
(The community FM transmitters that shared the TVW7 site in my later job used composite stereo on a single Programme line.)
Unbeknownst to us at the site, part of the landline section had a failure of one stereo channel, so the phone techs rerouted that channel only, via another couple of hundred km to restore the service.
One of our techs, who was very much into Classical music, swore he could hear a phase error between the two channels.
We listened on speakers in the quite noisy Tx control room & "Told him he was dreaming."
He persisted, so "just to shut him up" we checked it.
In their wisdom, the EEs at the ABC & Telecom Australia had instituted a pilot system to operate Programme fail alarms.
This pilot was in the form of a low level 15kHz tone on each channel, R & L.
The alarm box at the TX end of the programme lines very kindly supplied an output of these tones, so comparing them with an Oscilloscope was easy.
Of course, he was right! the pilot tones were well out of phase.
The phase error on lower frequencies would obviously be less, but to a "golden eared" person, it was discernible.
On another occasion, at a different place, another audio enthusiast told us that there was intermittent noise on the stereo sound signal from a Commercial TV Tx.
Again, we all listened, hung a 7L12 spec an off the aural exciter, but couldn't either hear it or see it.
At that juncture I had a couple of days off, & returned to find that the guy standing in for me had been called out when the exciter went crazy, spilling white noise right across the sound channels.
Again, the person who was seriously listening in a quiet environment warned about a problem that was not evident to people in a noisier situation, even though they were actively listening for it to happen.
I think the 7L12 wasn't quite up to the job, although I used it later to find interference on a composite FM stereo signal.