Yes, you can turn off Social chats & search monitoring.
To Turn off social chats & search monitoring,
Tap on the child and go to the 'Rules' page
Go to the 'Monitoring & Apps' tab on the top right
Tap on 'Social media monitoring' and toggle it off.
Related Questions;
Can I turn off 'Social Chats & search monitoring' for individual Apps?
Yes, you can turn off social media monitoring for individual apps.
To turn off Social chats & search monitoring for individual apps,
Tap on the child and go to the 'Rules' page
Go to the 'Monitoring & Apps' tab on the top right
Tap on 'Social chats & search monitoring' and make sure that it is turned on
Tap on the 'Monitored apps' on the right side
Toggle off the apps of your choice
This way, you'll not receive notifications for suspicious activities on those apps.