
Figure 1. Cathode ray tubes work be sending a beam of electrons from the cathode to the phosphor coated screen. Beam position is controlled by deflection using electric or magnetic field. Image: Cathode-ray tube on Wikipedia.
The important point here is that there is a beam of electrons moving through open space and these can be deflected. When semiconductors such as transistors came along the term "solid-state" came into use to describe the electronics as made of solid components without vacuum tubes.

Figure 2. The Hall-effect.
If an electric current flows through a conductor in a magnetic field, the magnetic field exerts a transverse force on the moving charge carriers which tends to push them to one side of the conductor. This is most evident in a thin flat conductor as illustrated. A buildup of charge at the sides of the conductors will balance this magnetic influence, producing a measurable voltage between the two sides of the conductor. The presence of this measurable transverse voltage is called the Hall effect after E. H. Hall who discovered it in 1879. Source: Hyperphysics.
So, magnetic fields can affect charged-carrier movement in solid-state devices and this is used to advantage in Hall-effect sensors in current measurement and magnetic position sensors (on industrial pneumatic actuators, for example). In most electronic applications magnetic field effects are far too small to cause problems.