Twisted pair EM immunity similar to earth magnetic field

Is it true that the mechanism by which twisted pair itself is immuned from EM noise similar to how earth is protected by the sun radiation by its own magnetic fields?

These are two different things. The constant magnetic field deflect the solar particles and radiation to the polar regions where there are fewer mammals to be damaged by them.

Twisted pair causes the induced signals to be common mode which can be eliminated at the far ends of the cable with transformer coupling.

No - twisted pair wire rejects noise by presenting adjacent sections of the wire pair that are reversed with respect to an incident magnetic field. The reversal of direction causes any induced current to be cancelled by opposite induced current in the next twist.

Protection of the earth from solar radiation takes two forms. The first is atmospheric shielding resulting from direct particle collision and/or interaction with ionized and non-ionized atmospheric gases, and the second is by magnetic deflection of charged particles.

Particles entering a magnetic field with velocity perpendicular to the magnetic field are subjected to a force which serves to move the particles in a circular path. The magnetic force acting on the particle always remains perpendicular to its velocity.

The magnitude of the magnetic force is F = q V B , where q is the magnitude of the charge of the particle, V its velocity, and B is the magnetic field.

The twisted pair works by cancelling induced current by physically reversing the direction of the wire "loop", and the earth's shielding works because of the action of the earth's magnetic field on a moving charged particle.

these are 2 different problems.
the twiste pair using to reduce the Inductive pick-up
near the equipment.