I would expect higher frequency crystals (MHz) to be much more immune than low frequencies (tens of kHz). Vibrations from machinery etc. don't tend to be extremely high frequency so the effect during a given cycle of the oscillator is small. However 'small' is not enough in applications with high vibration and sensitivity to phase noise such as some radar applications.
Many, if not most, consumer clocks use 32.768kHz tuning fork crystals because they are cheap and the oscillators can easily be made to be low power, even with 1970s technology. There does not appear to be a lot of information out there on their sensitivity. They are known to be prone to damage in ultrasonic cleaners and have a significant moving mass so I would expect high sensitivity to a narrow spectrum and in certain axis.
There exist MEMS oscillators which use a much higher frequency mechanical oscillation and divide down the output to emulate a 32kHz oscillator, however even they caution against ultrasonic cleaning of the product. Modern IC technology has yielded products that run on very low current as well (albeit with some other environmental sensitivity as a result).
If you need clocks to be 'completely' synchronous, you can provide synchronization by communicating between them (eg. via a wire or via some protocol such as PTP over a communication channel) or by using a common clock source or synchronization source such as from a GNSS ( Global navigation satellite system) system.