First, I believe the behavior you are seeing is normal. Note that the SDI is a differential input, if “nothing on input” means that the voltage at the SDI inputs is the same (SDI+ = SDI-), then small noise at the SDI inputs will make the SDO outputs switch. The signal they see at the SDO output is likely retimed noise from the SDI inputs.
Under normal operation, when SDI = logic 1 (SDI+ > SDI-) the SDO will be logic 1, and when SDI = logic 0 (SDI+ < SDI-) the SDO will be logic 0. Typically between data bursts the burst-mode receiver sets SDI to logic 0. The typical timing diagram is shown below, taken from page 3 in the MAX3634 datasheet.