I'm guessing that there's a missing

Set<Id> prodIds = new Set<Id>();

somewhere in the code. 

The reason you're getting the "SObject row does not allow errors" is because you can only add an error to the object that is a part of the Trigger context, so when you do this: 

allProdIds.addError('test'); 

it works because you're iterating through trigger.old.

However, later on (presumably line 46) you have this: 

for(product2 p:[select id, name FROM product2 where Id IN: accpids]){
               p.addError('Account associtated. Cannot delete this product');
               }

 Which will not work, because "p" is not a part of the trigger context.

You should be able to do this, however:

for(product2 p:[select id, name FROM product2 where Id IN: accpids]){
               product2 errObj = Trigger.oldMap.get(p.Id);
               if(errObj != null){ // probably unnecessary to null check this, but just in case...
                   errObj.addError('Account associtated. Cannot delete this product');
               }
}

Here's my re-write of the code you've provided:

if(Trigger.isDelete && Trigger.isBefore){
	Set<Id> setRateID = new Set<id>();
	List<Id> accPids = new List<Id>();
	Set<Id> prodIds = trigger.oldMap.keyset(); // as pjcloud mentions, no need to collect these

	// This will add an error to all objects in the trigger context, which
	// will prevent DML operations downstream; leaving this in for your test
	for(Product2 allProdIds:trigger.old){
		allProdIds.addError('test');        
	}

	// don't really need to check if(!prodIds.isEmpty()), since if it
	// were empty the trigger wouldn't be firing

	//check accounts associated
	for(account a: [SELECT product__c FROM account WHERE Product__C IN :prodIds]){
		accPids.add(a.product__c);                                
	} 
              
	//Remove ProdIDs from delete list that has Account association
	prodIds.removeAll(accPids);                         
             
	for(product2 p:[select id, name FROM product2 where Id IN: accpids]){
		// get the product2 from the trigger context and add an error to it:
		Trigger.oldMap.get(p.Id).addError('Account associtated. Cannot delete this product');
	}
         
	if(!prodIds.isEmpty() || prodIds.size() != 0)  {
		for(Product_Rate__c delRateObj :[SELECT Id from Product_Rate__c where ProductID__c IN : prodIds]) {
			setRateID.add(delRateObj.id);
		}                 
                                    
		if(!setRateId.isEmpty())
			ProdTriggerHandler.OnBeforeDeleteProd(setRateID);
	}
}