An active filter, i.e. which contains a power source, i.e. an op-amp, can be inductor-free. This is important for audio circuits where the frequencies are low and the inductors are huge and lossy due to their internal resistance. Consider the design for a 20Hz 4-th order filter and it can be either $2 of op-amp and capacitors fitting in 20x20mm, or it will be hundreds of dollars of inductors that take up perhaps a few litres of space and being horribly inefficient due to parasitic resistance in the inductors.
For radio frequencies however, the frequencies are often much greater than the bandwidth of any op-amp that you can buy. So while theoretically you could build an inductor-free filter using an ideal op-amp, there is no such thing as an ideal op-amp. You can't buy an op-amp with 100GHz of gain-bandwidth product! In other words, once you get up to higher frequencies, the op-amp has no gain any more and your filter won't work.
Happily though at radio frequencies, the inductors can be really really small. And by small, I mean surface mount and about a cubic millimetre of volume. So all the drawbacks of inductors at low frequencies are no longer relevant, and there is no real need to build inductor-free filters.
Radio filters can also implemented using tracks on printed circuit boards, which are themselves inductive. By using careful PCB track placement, you can create a microstrip filter which uses the parasitic inductance of the track and the inter-track capacitance to create your desired filter.