My core cannot upgrade to 2.0, my system won't run it, but my remotes on iPhone and iPad did

I’m afraid your Mac is running outdated software. 2.0 now requires 10.15.

If you plan to keep your system as is, you’ll need to downgrade all your devices to 1.8 (Legacy).

If you follow this guide, you’ll be able to go back to 1.8 (Legacy).

Download Links for Roon Core 1.8 (Legacy):

MacOS All-in-one / MacOS Remote

MacOS RoonServer

Windows All-in-one / Windows Remote (x64)
Windows All-in-one / Windows Remote (x32)

Windows RoonServer (x64)
Windows RoonServer (x32)

Download links for your Roon Remote (Legacy):

iOS App Store

Android Play Store
Android Manual Install (Link to APK)