Hi Andrew Martyn,
We appreciate you reaching out to us. We understand that you are looking to stop receiving Screen Time request via iMessage because you are experiencing performance-related issues with the Messages app.
We are committed to making sure that you get the most out of your Apple devices and services.
If you would like to troubleshoot this issue, we recommend that you start by restarting the devices.
- Restart your iPhone - Apple Support
- Shut down or restart your Mac - Apple Support
Also, let’s check for a software update and make sure that you are running the latest version of iOS and macOS.
While it isn't inherently assured that an update will resolve the issue, updating to the latest software version for your device can help isolate potential software issues.
On your iPhone, kindly secure a backup and update.
- How to back up your iPhone, iPad, and iPod touch
- Update your iPhone, iPad, or iPod touch
On your MacBook Pro, kindly secure a backup first if possible.
Then, update to the latest supported macOS version of your device, and let us know if the update helped.
- Back up your Mac with Time Machine - Apple Support
- Update macOS on Mac - Apple Support
Checking if the issue persists on safe mode may also help.
Performing this step may help resolve the issue, or further isolate the issue.
How to use safe mode on your Mac
If you want to make changes on request settings in Screen Time on Mac, please follow the steps below.
- "To change these settings on your Mac, choose Apple menu > System Settings,
- Then click Screen Time in the sidebar. (You may need to scroll down.)
- Click the Family Member pop-up menu on the right, choose the child that requested more time, then click Requests."
You can use the article below as a reference.
Change Requests settings in Screen Time on Mac - Apple Support
Take care!