Active antennas often send DC down the coax to power a remote amplifier circuit. They also typically have a DC blocking capacitor on the bias tee injection circuit to block DC being sent to the receiver. Yours seems to be missing that. You have to wonder what else it is missing.
Many (most?) radios have a capacitor on the RF input, which also would act to block the DC. If yours has that, it should be OK. If it doesn't, then yes, the radio could be damaged.
You could always add your own capacitor inline to the radio connection, to block DC. The value depends on the frequency range, from memory something like 0.1 uF should be OK?