According to this thesis the most common type of accelerometer used in MEMS is the capacitive one, and it has a natural/resonant frequency of "a few kHz".
The info that capacitive MEMS accelerometers are the most common ones also appears in here. So if the aforementioned thesis is wrong with respect to the frequency (which it might be given Spehro Pefhany's answer), you could at least survey some capacitive MEMS datasheets and derive your own range/statistics. Looking at this paper at least some academic ones have indeed a resonant frequency of only a couple of kHz. As another datapoint the datasheet of ADXL105 gives a min of 13kHz, typical 18kHz, and no maximum stated. You may not be so lucky with manufacturers other than AD; I've looks through a few of ST's MEMS accelerometers but they don't seem to give this data [resonant frequency] for any of them. I suspect the reason is that for [MEMS or otherwise] accelerometers the resonant frequency isn't important enough to tell the users, because they can only be used well below that.
Moving to gyros, according to this book there are three common types of MEMS gyros: tuning fork, vibrating wheel, and wine-glass resonators. So you could apply the same methodology to each those. For the vibrating MEMS gyros in general, this paper gives the resonant frequency as 10 kHz to 30 kHz as the most common range. Vibrating gyros are actually designed to vibrate at their natural/resonant frequency. The paper has a graph with both academic and industry devices; I suppose you're only interested in the latter, so you could filter out the graph's data accordingly.
Whether you'd be able to break any of these [accelerometers or gyros] just by externally forced resonance depends obviously on the amplitude of the external vibration as well. Unfortunately determining what amplitude they'd survive at their resonant frequency isn't so easy from datasheets. For accelerometers, you can certainly find the max g they can take, but this for non-repetitive motion/stress; e.g. for LIS3DSH this absolute limit is given as 10000g is for 0.1ms max, 3000g for 0.5ms. The paper I've taken the above graph from says their gyro could handle 1000g continuous external vibration below its resonant frequency [which was 100kHz], and in fact measure robustly in these conditions with error under 0.003°/s/g, but also says a commercial MEMS gyro had an error 1000 times higher, but they don't say at what max g they tested the commercial one.