Can AC in-rush cause problems for other devices on same circuit?
It is possible that transient voltages associated with starting and stopping the motor could cause problems. The power supply filtering for the electronic system should protect it from most transients on the power lines.

The first thing that I would look at is the routing of any input and output wiring for the electronic system. If any of that wiring is in the same conduit with motor power and control wiring that could easily cause problems. If the electronic I/O wiring is not in metal conduit and close to other wiring that is not in conduit, that could also cause problems.

Also any wiring or electromechanical control components in the same enclosure with electronic control equipment can cause problems.

All enclosures and metal conduits should have protective earth ground connections that are not shared with motor and motor control grounding connections.

There are a lot of possibilities.

Grounding and separation of electronic equipment wiring from power equipment wiring should be covered in the installation instructions for the electronic equipment. You should carefully read the installation instructions and inspect the installation to see if they have been followed.