FM stereo receiver, vintage 1973, has a noticeable background hoise
(hiss/white noise) on FM stereo regardless of the incoming signal level.
It
disappears completely upon switching to mono.

Noise in Stereo FM is out of phase between the channels, and thus
disappears when the signalchannels are added to mono.

That I knew...

Is this normal in a receiver of that age? If not, what components are
likely to be deteriorating?

This is not about age - rather about quality, unless of course something
is broken and age, if it was left unused for an extended period of time,
may have caused some components to deteriorate. Have you just found or
gotten it or do you know for sure that it has deteriorated. Try adding
the elementary information: make and model, someone may then know
whether it was likely to have been good or bad ex works.

Nikko STA-5010. FM stereo demodulator is a UPC554C chip.

Circuit diagrams somewhere on www.covingtoninnovations.com/audio.

Thanks!