Can strong magnets cause permanent damage to RFID tags?
The magnetic field from a magnet is static. In order to induce a current and/or voltage you need a changing electro/magnetic field.

Typically the field that RFID uses for operation has a frequency of at least 120 kHz but typically 13.56 MHz. That's much faster than you can practically generate by physically moving the RFID card around a magnet.

So near a permanent magnet you would be inducing a field but with a much lower frequency. The RFID tags are much less sensitive for such low frequencies as the antenna will not pick up that low frequency very well. So not much energy can reach the RFID chip and it should be nearly impossible to damage it that way.

So as far as I can see there can be no issue.