I'd rather you remove the SELECT's inside of FOR primarily. You can enter in a infinite loop and your trigger will fail.
The values of the the lists are only being used as temporary values to assign to the Object in the trigger, and there you're not performing and DML statement to update the related Id's.

make sure that you're editing the values retreived by SOQL and put a Database.update(SObject) to be done.

However once you do this you must avoid the recursivity because you'll enter again at the same trigger.

I didn't tested this code, but this is an idea how you can accomplish this:

​trigger PopulateRegion on Shipment_Order__c (before insert, before update) {
    
    
    Map<String, String> mShipto = new Map<String, String>();
    Map<String, String> mhubShipTO = new Map<String, String>();

    String queryString = 'Select Id from Ship_To__c WHERE';
    String whereConditionShip;
    String whereConditionHub;

    for(Ship_To__c vShipTO : Trigger.new) {
        mShipto.put(vShipTO.Ship_From_Zone1__c, Ship_From_Country__c);
        mhubShipTO.put(vShipTO.Hub_Ship_From_Zone__c,vShipTO.Hub_Country__c);

    }

    for(String zone1 : mShipto.keySet()) {
       whereCondition += ' ' + Ship_From_Zone1__c  = \'' + zone1 + '\' AND Ship_To__c = \'' + mShipto.get(zone1) + '\';

    }

  
    for(String mHub : mShipto.keySet()) {
       whereConditionHub += ' ' + Ship_From_Zone__c  = \'' + mHub + '\' AND Name = \'' + mhubShipTO.get(mHub) + '\';

    }
    
    List<Ship_To__c> shipto = Database.query(queryString + whereCondition);
    List<Ship_To__c> hubshipto = Database.query(queryString + whereCondition);

    
    for (Shipment_Order__c shipmentorder : Trigger.new) {
      
        If(shipmentorder.Hub_Shipment_Formula__c == False && shipmentorder.Ship_From_Country__c != null && shipto.size() > 0 ){

            string region = Country_Region_List__c.getInstance(shipmentorder.Ship_From_Country__c).Region__c;
            shipmentorder.Ship_From_Zone1__c = region; 
            shipmentorder.Ship_to__c = shipto[0].Id;
        }
        
        
        if (shipmentorder.Hub_Shipment_Formula__c == True && shipmentorder.Hub_Country__c != null && shipto.size() > 0)  { 
            
            string region = Country_Region_List__c.getInstance(shipmentorder.Ship_From_Country__c).Region__c;
            string hubregion = Country_Region_List__c.getInstance(shipmentorder.Hub_Country__c).Region__c;
            
            shipmentorder.Ship_From_Zone1__c = region; 
            shipmentorder.Hub_Ship_From_Zone__c = hubregion; 
            shipmentorder.Ship_to__c = hubshipto[0].Id ;
            shipmentorder.From_Hub_Destination__c = shipto[0].Id ;
            
        }
        
    }
    
}