Apple are implying that Audacity needs to be updated, but that is not strictly true (alternative fact 
).
Apple are wanting to abandon support for 32-bit software, but there’s still a lot of 32-bit software in use, so they are putting up a big scary message any time you run 32-bit software, saying that the app needs to be updated “to improve compatibility”.
Despite the warning, Mojave still supports 32-bit apps, but it is the last version of macOS that will. Apple have said that they are abandoning 32-bit software after Mojave.
All versions of Audacity for Mac to date, are 32-bit. The next version of Audacity (2.3.1) is planned to be released as a 64-bit application for Mac.
It’s probably nothing to do with 64-bit / 32-bit.
It’s more likely to due to the new “security features” in Mojave. By default, Mojave disables access to all recording devices for all software except for Apple software. For non-Apple software, you have to manually set the privacy settings for the “microphone” to allow the application to access the recording device. That’s what this post is about: No signal from USB turntable (Mojave) [SOLVED] - #6 by SonArc