Input transition time of 74HC4046
Typically, when you have minimum edge rates specified it is because that signal is interacting with an internal clock or signal in a way that might generate dangerous signals.  Looking at the data-sheet the INH (Inhibit) pin goes directly into the VCO, which probably means that a slow slewing INH input would cause runt pulses, for example.  You'd need more detail to be sure.

The SIGin input goes to a buffer , so presumably that will shape things up nicely for subsequent processing.

In general if the data-sheet mentions something, you should follow it.  If it does, then you can ignore it.  Especially in such an old design, like this part.