brassplyer wrote:
I've got a 70's era washer and dryer that I got used in the late 80's.
The drum sliders on the dryer have worn and the drum is at a low
angle, the transmission on the washer finally gave up the ghost.

I can get a replacement transmission for the washer and renovate the
drum sliders on the dryer, but it occurs to me that besides the
hardware, there's also 30-plus year old electrical components. I
wonder if at a certain point appliances become dangerous to keep
going.

I wouldn't worry about safety, except for parts related to the control
of gas in a gas dryer. It's possible the wire insulation has become
brittle and can easily crack, but that shouldn't be much of a hazard
since the appliances are grounded and made with metal housings.
However I'd probably replace an appliance if its wire insulation was
bad in many miscellaneous areas, as opposed to just one spot, unless I
was in the mood to completely rewire it.

The problem I have with new appliances is that they all seem to
utilize computer chip/circuit board technology. One of the great
things about the old washer/dryer is they utilize relatively simple
mechanical controls which appear to have contributed to their
longevity.

Electronic controls aren't that bad and can be repaired, unless a
custom-programmed chip fails. I don't know if such chips are
available, but they were for TVs. Common electronic problems are worn
pushbuttons, cracks in solder and circuit board traces, bad
capacitors, and shorted power components.

Does anyone still make rock-solid barebones washers and dryers with
mechanical controls?

Roper, a Whirlpool brand, offers nothing else, but mechanical controls
are still widely utilized in dryers and top-loading washers.