It’s a “feature”, not a bug.
Since Mojave, Remote Desktop control applications have to be given explicit permissions to be allowed to control the desktop.
We use Screenconnect. To get that to work with Mac Mojave, we have to go into System Preferences > Security > Accessibility and add the Screenconnect app to the list. You can probably do the same with remote control. After doing that we can then control the screen.
There are two gotchas that we’ve come to expect, even after adding our Remote Desktop app to the list. One, if the Remote Desktop app changes even slightly, such as with an app update, you have to get the user to go back into System Preferences > Security > Accessibilty. Once there, they have to first uncheck the Remote Desktop app, then recheck it. That really because it requires the user to have Admin privileges.
Second, you know that “Allow” button you have to click in the Security Preferences panel whenever you need to install new software? Yeah, Apple has made it impossible to click it using any Remote Desktop software. You physically need to be in front of the Mac and click it with the attached mouse. There is no other way. That’s mildly irritating when you have to ask the user to do it for you. It’s a security risk to give them admin rights to do it for you. It’s a straight up inconvenience when you have to drive to a site with a monitor, keyboard, and mouse to click that button on a normally headless Mac Pro Server sitting in the closet.