Frequency spacing and the doppler effect
When moving at 1km per second (very fast for anything using a road) a radio wave of carrier frequency 100 MHz will appear to shift to 99.9997MHz if traveling away from the source of the transmission. This is a deviation of 300 Hz.

Satellites (such as ISS) travel at 7.66 km/sec so therefore the 100MHz appears to be 99.9974MHz i.e. a deviation from the nominal carrier centre of 2.6 kHz.

Typical FM communication channel separation might be as low as 12.5 kHz so there's good reason to suspect high speed being a potential cause of poor reception BUT, at an offset of 2.6KHz I believe an FM receiver should easily cope with aligning itself with the apparent off-centeredness of the transmission. They use PLLs for keeping aligned to transmissions so I don't think it will be a problem.

For a simple radio system like one running at 434MHz there will be a dc shift in the demodulation output but given that a lot of these transceivers are low precision (relying on a data slicer for extracting the data from the raw demod output), I don't see it as an issue. They have a receive bandwidth of over 1MHz so it should be easy to see it won't be an issue.