I have been using Mojave without problems, so it does work. It sounds like you may need to reinstall the montage Yamaha-Steinberg driver and the new montage connect 1.05 for Mojave. Here is a link to those files: https://usa.yamaha.com/products/music_production/synthesizers/montage/downloads.html

I am also using Mojave. Montage usually works. I have an issue with Cubase which does sometimes not get the audio connection to the Montage. A reboot then helps. Standalone Kontakt always works, though.

Montage/Mojave user here. Everything works as expected.

Thank you for letting me know that everything is working for you guys, I am running down the entire gambit of "duh" solutions again to make sure I'm not that "I switched the USB cable and it works" guy.
If anyone has suggestions based on the fact that with High Sierra and Montage V2.5 everything worked properly, and the Mojave update is the only variable I can identify when everything stopped communicating, I would be in your debt.
I have another person experiencing this problem as well. I will report back here when I find the solution. I will keep checking this thread in case someone knows what is happening.
Be well, friends.

Try checking the following...
Go to “System Preferences” > find the red icon for the “Yamaha Steinberg USB Driver” > double click to see the “About” screen... what does it report?

Try checking the following...
Go to “System Preferences” > find the red icon for the “Yamaha Steinberg USB Driver” > double click to see the “Aboutl screen... what does it report?

"Yamaha Steinberg USB Driver V1.10.2"

This may not apply, but Steinberg has the following note on MacOS:

Important information on the installation on macOS High Sierra and Mojave.

https://helpcenter.steinberg.de/hc/en-us/articles/115001790330-macOS-Systemerweiterung-blockiert-Hinweis-bei-der-Installation-von-Hardware?_sp=a847ddbb-40ce-4242-9629-88af9532ac87.1543374476836

Yamaha Steinberg USB Driver V1.10.2

Driver has installed fine.

In your DAW (?) what happens that makes you say "everything stopped communicating"?
What DAW are we talking about?

The Driver seems to be communicating with Mojave.

This may not apply, but Steinberg has the following note on MacOS:

Important information on the installation on macOS High Sierra and Mojave.

https://helpcenter.steinberg.de/hc/en-us/articles/115001790330-macOS-Systemerweiterung-blockiert-Hinweis-bei-der-Installation-von-Hardware?_sp=a847ddbb-40ce-4242-9629-88af9532ac87.1543374476836

The message indicating that the Driver was blocked did not appear in this panel. I went to the firewall settings and manually included Steinberg Driver, allowed connections, and nothing improved. I've included screen shots to avoid confusion...

Yamaha Steinberg USB Driver V1.10.2

Driver has installed fine.

In your DAW (?) what happens that makes you say "everything stopped communicating"?
What DAW are we talking about?

The Driver seems to be communicating with Mojave.

And that is the confusing part! To clarify "everything stopped communicating" I am indicating that prior to updating, Montage not only worked inside all of my DAW's as an audio input device (which could be selected similar to an audio interface) but it also connected as a MIDI device, the simplest communication possible between the keyboard and my Mac.
Now, NOTHING is recognized, not audio, nor MIDI input.
To add to this confusion, I plugged in my Yamaha MX61 and it worked perfectly fine, a connection that requires an active Steinberg USB Driver! I've included a screen shot of my Mac MIDI device settings, you'll see that the Ableton Push 2, iConnectivity box, and Yamaha MX61 are all lit and functioning properly. You'll also notice the dark, sad, and forlorn Montage up there, inactive. This is only present due to effectively connecting before and making a profile on this computer before the update.
See attached:

Let’s try this another way. Is Cubase among “all of my DAW’s”?

Let’s try this another way. Is Cubase among “all of my DAW’s”?

Cubase is not one of the DAW's.

Pro Tools, Reason 10, Ableton 10, Logic Pro X, and Garage Band were all tried though.

What were you thinking?

I'm not sure what has been attempted before - if you tried an in-place re-install of the driver (meaning you did not uninstall the driver first before reapplying the driver install). If you have not already done this, I see value in uninstalling the driver. I'm not familiar with Mac - but in the PC there's a mechanism to uninstall a driver so you can reboot fresh with no Yamaha Steinberg Driver. After rebooting with no driver installed - I would re-install the driver.

The thought I would have (thinking in PC terms - so this may have a parallel concept in Mac) is that the OS upgrade may have "messed up" registry settings for the driver and that uninstalling the driver would "clean house". Then installing the driver from a fresh system would properly populate those settings where an in-place re-install would inherit some bad settings.

Cubase is not one of the DAW's.

Pro Tools, Reason 10, Ableton 10, Logic Pro X, and Garage Band were all tried though.

What were you thinking?

I'm thinking, none of your screenshots is of "one of the DAW's" setup. I'm not sure what we are to gather from the screenshots you are showing us. Try selecting the Yamaha Steinberg USB Driver from within one of those DAW's... with Cubase you don't have to deal with anything outside of the Cubase Setup... you negotiate it all from within the actual DAW program. It does NOT require you to do anything with the computer's setup outside of the DAW application to get things setup.

Please show us a familiar SETUP screen in any one of the many DAWs
Can you "see" the Driver within one of those many DAWs?