In the Qi standard, frequency is listed as 80-300kHz for the higher power application which is within the target(resonance?) frequency of LF RFID tags. So power transmission should be quite high for the tags. Will this damage the tags or can they just ignore the induced current?
Qi chargers do not continuously transmit power. There is a communication and negotiation sequence that occurs to establish what the receiving device requires before the power transmission is started.
The communication will happen at much lower TX power levels to ensure this kind of a problem doesn't occur and when power transmission is in progress the transmitter performs foreign object detection (in case something conductive like an RFID tag gets in the way) and infers the efficacy of the coupling between TX and RX coils to make sure it should continue transmitting power.