Arduino Micro is 8-bit and SparkFun MPU-6050 is 16-bit.
The two specifications mean totally different things. The Micro has an 8 bit data bus. The MPU data output is 16 bits. It just means that to read a MPU the Micro has to transfer 2 8 bit words. Look at any example code that reads a MPU.
If they are both 3.3V then they can be interfaced, directly, via the I2C bus. If one does need to interface via I2C two different bus voltages, level shifters are easy to implement.
does it matter if that bitrate/bandwidth is different?
What do you mean by that? If they are both 5V and I2C they should work together. The only bitrate that is relevant, here, is the I2C clock (SCL).
Is open source electronics generally compatible?
That is such an open question that the answer has to be, maybe. The only way to insure compatibility is to carefully study the specifications.
groundFungus:
The Micro has an 8 bit data bus. The MPU data output is 16 bits. It just means that to read a MPU the Micro has to transfer 2 8 bit words.
Is that bit transfer any kind of problem? Have to do something with code/libraries?
Is that bit transfer any kind of problem? Have to do something with code/libraries?
No, none. You just do 2 reads and reassemble the 2 bytes back into an int (16 bits). Look at any of the examples for reading the sensor to see how. Some libraries do it for you.