Spectrum management is both science and art. One way of avoiding interference is using separate frequencies for different systems. If the spectrum can be confined to national boundaries, then usually it is licensed by the country administration (FCC, Ofcom etc.) however, if you want to operate a global system, the allocation must be done on an international level via the ITU.
SpaceX applied (see page 4) for spectrum roughly in the 10-14 Ghz. This band is not used by mobile phones. It is also not used by medium wave radio broadcasting because it is, well... microwaves and not medium waves. Marine radio uses the VHF band and HF, again - not microwaves, so the systems shouldn't interfere in any way. I don't know about marine radars though.
Reuse of satellite spectrum on the ground generated some signifficant controversy.
Avoiding terrestrial systems is the "easy" part. What requires careful consideration are other satellite systems. The Ku spectrum SpaceX applied for is already in use by other satellites, however because microwaves are highly directional compared to other frequencies (think of a laser beam vs. normal light bulb), you can carefully reuse the spectrum. Imagine pointing two laser beams in totally different directions - the waves won't interfere, because they physically are not in the same space.
SpaceX's system will use phased array antennas (page 5), which basically can "move the signal around" without physically moving the antenna. When the satellite flies over the ground station, the station will point its beam at the satellite and vice versa. Of course the antenna system is not perfect, so there will be some "spill" (called sidelobes).
A satellite dish used for receiving TV has very high gain in one direction (and limited "field of view"). It will basically "not see" a Starlink satellite, unless it flies directly through the path between ground and the geostationary broadcasting satellite. Even when this happens it will likely be very short. Such interruptions may be already taken into account, because the sun causes periodic loss of communication with geostationary satellites.