Typical FMCW radars transmit very short ramps (microseconds) at a very long (relatively) intervals (several ten milliseconds), i.e. a duty cycle of less than 0.1%.
In order to create interference between two radars, the ramps have to overlap pretty exactly, within a few nanoseconds of each other. This is very unlikely to happen.
Modern radars employ technologies to detect and/or avoid such collisions.
Overall it is not really an issue, even with many radars in crowded spaces.
This is true for some earlier lofi radars, but as driver assistance and self-driving have developed, so have the requirements and capabilities of the radar systems. Newer systems generally have shorter PRIs for higher doppler bandwidth, and much higher duty cycles for more energy on target - the FCC limits power, so you've got to get energy from the time axis. Both of these things make the interference problem harder.
In practice, the difference between pulsed radar and continuous wave radar is a continuum rather than a dichotomy. Historically, FMCW (frequency modulated continuous wave) had a high duty cycle (though not 100%, the ramp generators need finite time to reset (though you can alternate between up and downramps and get closer)). For some applications, though, requirements force you to short ramps and long PRIs, thus low duty cycles, but the name (FMCW) sticks.
In order to create interference between two radars, the ramps have to overlap pretty exactly, within a few nanoseconds of each other. This is very unlikely to happen.
Modern radars employ technologies to detect and/or avoid such collisions.
Overall it is not really an issue, even with many radars in crowded spaces.