Need circuit to permit the lowest frequency of two input signals and stop the other one (audio)
Using a flip flop to divide a frequency means you're not really doing this analog, anyway: your discretizing amplitude to feed it into the flip-flop, and the flip-flop handles your signal as discrete in time, so congratulations, while claiming this is an analog solution, you basically invented a digital system!
So, yeah, this is easy with a digital signal processor, which these days means &quot;basically any 1-2 € ARM microcontroller with at least 2 ADC channels&quot;.
That would put your component count to 9 to 11:

1 Microcontroller
2 R + 2 C for one RC antialiasing filter and one RC reconstruction filter
a dual opamp (optionally) to drive your filter and ADC and to buffer the output
1 or 2 decoupling capacitors

assuming your microcontroller has a sufficient DAC; else, add a DAC (and a decoupling capacitor) to the equation.
The rest is classical digital signal processing: use a Welch detector to detect your dominant tone, and a linear-phase FIR filter to blank the recessive tone on detection.
Latency might be a problem: to determine whether a tone of 120 Hz is played, you'll really need to observe for at least half a period, more realistically 1 to 10 periods. This means you might very well incur a significant time difference between onset of dominant tone and muting of the other.
You'll also want to delay your signal by half the length of the blanking FIR filter when passing it through – that's the filter's group delay, and you'd make temporal &quot;jumps&quot; whenever you switch between blanking and non-blanking otherwise. (That's not a special &quot;problem&quot; of the digital filter: an analog filter has a group delay, too, just that we can't make it constant over all frequencies as in a digital filter, necessitating way more effort on mode switch than the digital approach.)