Can the inrush current of a DC motor powered by a battery affect/damage other devices conected to the same battery?
The problem isn't different devices demanding different amounts of current. Mainly, the issues you may encounter are:


Voltage/current drops caused by the motors that may affect sensitive devices powered from the same source. For this you must make sure using batteries rated for currents (with some margin), required by the motors. Another measure is installing bulk capacitors near the sensor, it will guarantee correct voltage/current to the sensors in case of short voltage drops caused by the motors. For this, the bigger the capacitor the bigger will be protection. Of course using too large ones for the application will be a waste of money and space.
Noise: Inductive loads causes lots of noise on the power rails. For this you can protect the sensor adding capacitors with the right values across motor input poles. Like Methods of filtering noise caused by DC brush motors e.g. It looks coherent that you add also noise protection near the sensor.
Inductive fly-back: This is very important. Commuting DC motors OFF generates voltages spikes that are far away greater than other parts connected can take, like sensors. You can waste your sensors easily without protection to this.
Refs:
https://www.westfloridacomponents.com/blog/inductor-need-fly-back-diode/
https://en.wikipedia.org/wiki/Flyback_diode
It's very important that you check the range finder datasheet for recommendations, absolute maximum rates or other precautions not listed here required by the sensor.