Are you running SEC On-Prem? We had issues with this in version 9.9.5 and they admitted there was something wrong with the check for prompting full disk access, and pushed us to 9.9.6.
After 9.9.6 we dont see any Pop-ups. Talk to your Sophos Rep to get 9.9.6.
Here are our settings.
com.sophos.SophosScanAgent
identifier "com.sophos.SophosScanAgent" and anchor apple generic and certificate 1[field.1.2.840.113635.100.6.2.6] / exists / and certificate leaf[field.1.2.840.113635.100.6.1.13] / exists / and certificate leaf[subject.OU] = "2H5GFH3774"
SystemPolicyAllFiles - Allow
com.sophos.macendpoint.CleanD
identifier "com.sophos.macendpoint.CleanD" and anchor apple generic and certificate 1[field.1.2.840.113635.100.6.2.6] / exists / and certificate leaf[field.1.2.840.113635.100.6.1.13] / exists / and certificate leaf[subject.OU] = "2H5GFH3774"
SystemPolicyAllFiles - Allow
com.sophos.macendpoint.SophosServiceManager
identifier "com.sophos.macendpoint.SophosServiceManager" and anchor apple generic and certificate 1[field.1.2.840.113635.100.6.2.6] / exists / and certificate leaf[field.1.2.840.113635.100.6.1.13] / exists / and certificate leaf[subject.OU] = "2H5GFH3774"
SystemPolicyAllFiles - Allow
com.sophos.SDU4OSX
identifier "com.sophos.SDU4OSX" and anchor apple generic and certificate 1[field.1.2.840.113635.100.6.2.6] / exists / and certificate leaf[field.1.2.840.113635.100.6.1.13] / exists / and certificate leaf[subject.OU] = "2H5GFH3774"
SystemPolicyAllFiles - Allow
com.sophos.autoupdate
identifier "com.sophos.autoupdate" and anchor apple generic and certificate 1[field.1.2.840.113635.100.6.2.6] / exists / and certificate leaf[field.1.2.840.113635.100.6.1.13] / exists / and certificate leaf[subject.OU] = "2H5GFH3774"
SystemPolicyAllFiles - Allow