As of version 4.4, Hazel is compatible with Catalina. Catalina introduced a number of changes and bugs which affect Hazel. Hazel 4.4 works around many of these issues though some still remain, possibly indefinitely.
Most noticeably, dark mode is broken. There are limits to what can be overridden so as a result, certain places, like the System Preferences title bar and contextual menus, will remain in light mode regardless of your system appearance setting.
You will see magenta rectangles in certain windows. This is considered a “security feature” by Apple.
There may also be various drawing artifacts and oddness with mouse input.
For Hazel 5, Hazel will be converted from a preference pane to an app form factor. This will require re-working the UI. The end result is that this will avoid the issues described above as well as others that were introduced in Catalina. Note that version 5 is not due until the later part of 2020, at earliest.
If you have any questions or issues, please contact us via the Support page.