Oddly enough, in this case the crown ethers are acting as surfactants as well as ligands, and other surfactants can also be used. When the crown ether ligates to an ion, the inner surface of the ether contains all of the oxygens (polar functionalities) and interacts with the ion. The outer surface is non-polar, containing all of the hydrocarbon linkers, and can interact with the non-polar solvent.
Other surfactants do the same thing - they have a polar end and a non-polar end, the polar end can interact with the ions and the non-polar end can interact with the solvent. Crown ethers are very clever in that they can be tailored to form an interior ligating shell of the perfect size to interact with only a single type of ion, and are thus very selective for the ions they will solvate.