The following exception is thrown when sending emails and updating the users using apex with setSaveAsActivity set as true while sending emails.

Exception:

MIXED_DML_OPERATION, DML operation on setup object is not permitted after you have updated a non-setup object (or vice versa): User, original object: EmailMessage: []

Sample Code to reproduce the issue:

User objUser = [
    SELECT Id, IsActive
    FROM User WHERE Name = 'Test User'
    LIMIT 1
];

List < Messaging.SingleEmailMessage > listMessages = new List < Messaging.SingleEmailMessage >();
Messaging.SingleEmailMessage message = new Messaging.SingleEmailMessage();
List < String > listToAddresses = new List < String > { '[email protected]' };
message.setToAddresses( listToAddresses );  
message.setSubject( 'Testing Email' );   
message.setUseSignature( false );   
message.setHtmlBody(
    '<h1>Testing</h1>'
);  
listMessages.add( message );  

if ( listMessages.size() > 0 ) {

    Messaging.sendEmail( listMessages );
    
}

objUser.IsActive = false;
update objUser;

Use setSaveAsActivity( false ) to resolve the issue.

Sample Code to fix the issue:

User objUser = [
    SELECT Id, IsActive
    FROM User WHERE Name = 'Test User'
    LIMIT 1
];

List < Messaging.SingleEmailMessage > listMessages = new List < Messaging.SingleEmailMessage >();
Messaging.SingleEmailMessage message = new Messaging.SingleEmailMessage();
List < String > listToAddresses = new List < String > { '[email protected]' };
message.setToAddresses( listToAddresses );  
message.setSubject( 'Testing Email' );   
message.setUseSignature( false );   
message.setSaveAsActivity( false );
message.setHtmlBody(
    '<h1>Testing</h1>'
);  
listMessages.add( message );  

if ( listMessages.size() > 0 ) {

    Messaging.sendEmail( listMessages );
    
}

objUser.IsActive = false;
update objUser;