How to Connect a router to console, using a mac
I don't know if I am a "serious Mac user" but I do use my Mac "seriously".

The instructions you got fit pretty much all OSes (Windows, macOS, Linux).  It just depends on the software that you use

What those instructions are telling you is to use an RS-232 connection to talk to the router.  This type of maintenance has been around since at least the 1970s and predates macOS/OS X

The only "modern" difference is that they now recommend a USB to UART bridge, or in more common vernacular, a USB to Serial Adapter because modern computers haven't been shipping with RS-232 serial ports for a long, long time now (since USB became mainstream).

You won't need to install any software; you just need to use screen that is included with macOS.  You must go through Terminal because


screen only runs in Terminal
you are connecting to the pfSense console (which is, in effect, another Terminal connected to a serial port)


What you would then do is connect to the console by issuing the command:

$ screen /dev/cu&lt;USBdeviceName&gt;


I currently don't have one attached to my Mac so I can't show you an exact name.  Though, I do  have FreeBSD on an old Dell workstation for this with dedicated RS-232 ports and my devices are /dev/cuca0 and /dev/cuca2.  (OS X bases a lot of their inner working on BSD)  You will have to see what the device gets named by listing out /dev.