Unshielded speaker magnets will affect a CRT monitor by changing the display colours, especially at the sides close to the magnet. The effect will change or go away if you move the speakers.
CRTs, including TV picture tubes, are sencitive to magnetic fields, including the earth's magnetic field. Therefore they have what is called a degaussing circuit built in. This applies a strong alternating magnetic field for a brief moment on switching it on, and demagnetises the tube.
The automatic degaussing mechanism works only if it is switched on from a cold condition. But some monitor models also have provision to degauss the tube manually while it is on, in addition to the auto circuit.
Spealers designed for use with computers have shielded magnets that do not affect the CRT.