I wonder what the acceptable hz variation is for household current.
Not sure this is the question you want to ask. We used to run synchronous motor clocks off the utility main power and expect them to be accurate. Regardless the grid is very tightly controlled for HZ as all kinds of bad happens to the utility if the HZ varies. For example overload slowing the HZ down starts brownouts and blackouts to keep the HZ spot on. HZ to a utility is more important than voltage.
The Onan generator I listed above is 59-63 HZ depending on the load on it and it's governor control. Extreme idle stop is set at 54 HZ although it should never run at this HZ. Typical adjustment is for 59HZ minimum at full load: ideally 60 HZ at full load. (The engine governor needs some RPM (HZ) change to work properly.)
Most modern "Global" stuff, TV, computer, etc... their power supplies are rated for 50-60 HZ so it can run in other countries without changes. These are no longer sensitive electronics due to modern power supply designs.
AC Motors will simply follow the HZ and run at that speed although they may be out of their design range at some low or high HZ and could overheat or stall out.
I suggest you are asking about "Dirty Power" and specifically if a device you plug in will have problems on a generator.
For example I plugged in a HZ meter on my RV generator and found a surprising 400HZ reading. I turned on the air conditioner and found a normal 60 HZ. Turns out the 400HZ was "noise" from the "battery charger" converter interacting with the generator. It caused the old microwave in the RV to not power up on gen power and makes a new GFI light up an unhappy red light. If I run a AC motor the "noise" goes away and things work... It's said that some microwaves use the line HZ as a "clock" signal for their electronics. Clearly the old microwave was overwhelmed by the 400HZ noise.
@Dan_69GTX linked his post of waveforms showing clean vs. dirty waveforms. Noise from a bad load is beyond that, but, another angle of dirty power. Some generators are better than others in design of the regulator from CHEAP capacitor regulators to high end electronic regulators. "Sensitive" computers run very well on the awful APC UPS output waveforms.
As noted above there is no hard and fast rule on what is sensitive anymore and further the source of the "noise" or problem may not be the generator itself.