trigger updateContactOnEmailOptOutChange on Contact (after update) {                                                                                          
     
    //Initialize lists and maps

    List<Contact> duplicateContacts = new List<Contact>();
    Map<String, Contact> contactEmailMap = new Map<String, Contact>();
    Map<Id, Contact> contactIdMap = new Map<Id, Contact>();

    //Build a map with contacts to update. Only select the ones that have a different "Email Opt Out" value from the contact being updated.

    for (Integer i = 0; i < Trigger.new.size(); i++) {
        if (Trigger.old[i].HasOptedOutOfEmail != Trigger.new[i].HasOptedOutOfEmail) {
            contactEmailMap.put(Trigger.old[i].email, Trigger.new[i]);
            contactIdMap.put(Trigger.old[i].id, Trigger.new[i]);        
        }
    }    
    
    //Only go through this process if "Email Opt Out" (HasOptedOutofEmail) was updated.
    
    If (contactIdMap.size()>0) {
    
        //Query the database and look for all contacts with a duplicate email address (same email as the contact currently being updated).

        for (Contact dupContact : [SELECT Id, Name, Email, HasOptedOutOfEmail
                                   FROM Contact
                                   WHERE Email IN : contactEmailMap.KeySet()
                                   AND Id NOT IN : contactIdMap.KeySet()]) {
            Contact contact = contactEmailMap.get(dupContact.Email);
            If (dupContact.HasOptedOutOfEmail <> contact.HasOptedOutOfEmail) { 
                dupContact.HasOptedOutOfEmail = contact.HasOptedOutOfEmail;   
                duplicateContacts.add(dupContact);
            }
        }    
    
        //If any duplicate contacts were found, update all duplicate contacts with the new HasOptedOutOfEmail value.

       If (duplicateContacts.size()>0) update duplicateContacts;
   }
}

Batch Apex

global class updateContactOnEmailOptOutChange implements Database.Batchable<sObject>
{
    global string query;
   
    global updateContactOnEmailOptOutChange()
    {
    query = 'SELECT id,Name, Email, HasOptedOutofEmail from Contact where HasOptedOutofEmail=true';
    }
   
    global Database.QueryLocator start(Database.BatchableContext BC)
    {
    return Database.getQueryLocator(query);
    }

   
    global void execute(Database.BatchableContext BC, List <sObject> duplicateContacts)
    {
    Map<String, Contact> contactEmailMap = new Map<String, Contact>();
    Map <Id, Contact> contactIdMap = new Map<Id, Contact>();
   
    // Build a map with contacts to update. Only select the ones that have a different "Email Opt Out" value from the contact being updated.
    if(trigger.isUpdate){

    for(Integer i=0; i<Trigger.new.size();i++)
      {
      if(Trigger.old[i].HasOptedOutOfEmail != Trigger.new[i].HasOptedOutOfEmail)
          {
          contactEmailMap.put(Trigger.old[i].email, Trigger.new[i]);
          contactIdMap.put(Trigger.old[i].id, Trigger.new[i]);
          }
      }   
   
    if(contactidMap.size()>0)
    {
    //Query the database and look for all contacts with a duplicate email address(same email as the contact currently being updated)
    for (Contact dupContact: [SELECT Id, Name, Email, HasOptedOutofEmail
                              FROM Contact
                              WHERE Email IN: contactEmailMap.KeySet()
                              AND Id NOT IN: contactIdMap.KeySet()])
                                  {
                                  Contact contact=contactEmailMap.get(dupContact.Email);
                                  If(dupContact.HasOptedOutOfEmail <> contact.HasOptedOutOfEmail)
                                  {
                                  dupContact.HasOptedOutOfEmail = contact.HasOptedOutOfEmail;
                                  duplicateContacts.add(dupContact);
                                  }
                                  }
    // if any duplicate contacts were found, update all duplicate contacts with the new HasOptedOutOFEmail value.
   
    If(duplicateContacts.size<>0) update duplicateContacts;
    }
    }
    }
   
    //The batch process has completed successfully. Schedule next batch.
   
    global void finish(Database.BatchableContext BC){
    // //Build the system time of now + 300 seconds to schedule the batch apex.
    Datetime sysTime = System.now();
    sysTime = sysTime.addSeconds(300);
    String chron_exp=''+sysTime.second()+''+sysTime.minute()+''+sysTime.hour()+''+sysTime.day()+''+sysTime.month()+'?'+sysTime.year();
    system.debug(chron_exp);
    updateContactOnEmailOptOutChangeScheduler scheduleFieldUpdate = new updateContactOnEmailOptOutChangeScheduler();
    //Schedule the next job, and give it the system time so name is unique
    System.schedule('New Email Update Job'+sysTime.getTime(),chron_exp,scheduleFieldUpdate);
    }
    }