Bypass any rectifier diode with a 0.047uF polypropylene cap and it becomes an audio grade rectifier.
This statement is false. The old saw about bypassing rectifiers really doesn't work.
The problem is that the rectifier has a capacitance in its junction and the power transformer has an inductance. Together they form an electrical resonance usually at a pretty high frequency owing to the tiny capacitance involved.
Added more capacitance does not solve the problem- it merely moves the resonance down to a lower frequency.
This might not be an issue because the peak might not go into excitation. But if it does you get 'diode noise' (which is really coming from the transformer) that leaks about readily.
The solution is to bypass the input of the diode from the power transformer with a resistor in series with a capacitance to snub the resonant peak.
If this is done correctly then the choice of diode won't have much effect on the circuit as proposed in the quote.