Why are high frequency signals not disturbed by stray fields?
why the high-frequency signals are immune to EMI?


Not quite. Stray magnetic fields usually means things are more like magnets and coils in the nearby vicinity which are typically much lower frequency than your typical EMI.

It is not that inductive sensors operating at higher frequencies are somehow immune to being influenced by stray magnetic fields as it much as it is that stray magnetic fields are usually of much lower frequency and can therefore be distinguished from your signal of interest. Though I suppose technically it could also be that inductive sensors operating at higher frequencies are able to utilize much smaller inductances so lower frequency stray magnetic fields have to be that much, much stronger in strength (or faster, but that would make them high frequency magnetic fields which stray magnetic fields usually aren't) to induce the same effect on the signal.