1. Possession of electronic devices such as radio receivers (or transmitters!) is not prohibited aboard passenger aircraft. Using them is prohibited, so don't do it.

2. Contrary to what TA posted above, it's very unlikely that a radio receiver has an oscillator running at the frequency being received. It's far more likely that there is an oscillator running 10.7 MHz away from the frequency being received, not to mention several other oscillators. It so happens that the upper frequency limit of the FM Broadcast Band is much closer than 10.7 MHz from the lower frequency limit of the Aircraft band. In any event, it doesn't matter whether a particular radio interferes with aircraft communications or navigation equipment or not. It's just prohibited. In order to approve a radio for use, that particular model would have to be tested to prove that is does not cause interference from every possible location in every possible aircraft. (Aircraft antennas are located in various places along the fuselage.) This is obviously impractical and expensive to do even once (and of course cabin crew would have to know how to determine what type of radio you were using).