Everyone will be upgrading to 64 bit apps eventually, if you want to keep using future Mac operating systems. Apple insists on it. But this message is currently more for developers like Adobe than end users. For now, it's awareness for end users and a call to action for developers.
There will come a day when Apple stops 32 bit support completely. On that day, you stop updating your Mac operating system if you cannot live without your 32 bit app and there will never be a 64 bit version of it. If all your apps are 64 bit on that day then you'll be fine. But we're not there yet. Might be in 2019 or 2020. No-one knows the final date, not even Apple yet. We're in a very long grace period.
Apple's statement on the issue:
32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support
This warning (nag screen) will appear every 30 days when you launch a 32 bit app in Mojave. There is nothing for end users to worry about yet. It's part of Apple's decade long campaign to drop support for 32 bit apps. In this case, the ball is in Adobe's court to issue 64 bit versions of their apps - before Apple disables them entirely in the operating system. Adobe is no doubt working on it.
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So update your computer and carry on as normal for now.