There is a presentation that covers this subject which is a regular at the International VLBI Service workshops. The most recent version is at High-accuracy Time and
Frequency in VLBI and the relevant derivation of needed accuracy is on slide 5. Basically for interferometery, you are trying to match up the phase of the waveforms (position along a sine wave in the simplistic sense) of the two signals from each of the dishes.
If we use an observing frequency of 10 GHz (10e9 Hz) and want to keep the phase coherent to ~10 degrees (out of the 360 degrees) after 1000 seconds integration then you need 10 / (360 * 10 * 1e9 * 1e3) or 10 / 3.6e16 or a clock stability of about 2.8e-15. Higher frequencies such as the 230 GHz mentioned in the comment will be even more demanding.
If you look at Allan Deviation/Variance plots, which measure the stability of clocks, such as the plot on slide 4 (and copied below): this level of performance at 1000 seconds is only reached by hydrogen masers. The typical GPS Disciplined Oscillator will be at about 1e-12@1000seconds, see this recent comparison of 17 GPSDOs. With careful correction of the sawtooth error caused by the internal oscillator of the GPS (discussed at the end of the presentation) you can improve the typical 50 ns jitter of GPS to ~5 ns. Beyond this atmospheric/ionospheric effects come in and you need to use a dual-frequency GPS to take those out.