Thanks David! I do need the after Delete because there is another piece of the trigger that adds & removes values to the associated Account. I was only trying to address the finding duplicate values with this post as the rest of the trigger works as expected.

I replaced my code with yours but I got quite a few errors. I wasn't quite following the new code, so I'm not sure if these are typo style errors or something bigger.  Thanks for your help!

Line 30 - Invalid type argument count for Map: expected 2 but found 1
Line 31 - Method does not exist or incorrect signature: void contains(Id) from the type Map<Id,Set<String>>
Line 33 - Illegal assignment from Set<String> to Map<String>
Line 35 - Variable does not exist: existingTypes (which is odd because that is the name of the Map)
Line 36 - Method does not exist or incorrect signature: void put(Id, Map<String>) from the type Map<Id,Set<String>>
Line 43 - Method does not exist or incorrect signature: void contains(Id) from the type Map<Id,Set<String>>
Line 51 - Invalid type argument count for Map: expected 2 but found 1
Line 52 - Variable does not exist: existingTypes
Line 53 - Method does not exist or incorrect signature: void put(Id, Map<String>) from the type Map<Id,Set<String>>


 

trigger UpdateAcctVIP on VIP_Type__c (after insert, after update, after delete){

	Set<Id> acctIds = new Set<ID>();
	Set<Id> contIds = new Set<ID>();
	map<Id, set<VIP_Type__c>> contact_type_map = new map<Id, set<VIP_Type__c>>();

// Get all the Account & Contact Ids in the Set 
	if (Trigger.isDelete) {
		for(VIP_Type__c vip : Trigger.old){
			acctIds.add(vip.Account__c);
            contIds.add(vip.Contact__c);
//            contact_type_map.put(vip.Contact__c, new set<VIP_Type__c>());
		}
	}
	else{
        for(VIP_Type__c vip : Trigger.new){
			acctIds.add(vip.Account__c);
            contIds.add(vip.Contact__c);
//            contact_type_map.put(vip.Contact__c, new set<VIP_Type__c>{vip});
	}
    }
 List<VIP_Type__c> vipRecs = [SELECT Id,Account__c,Contact__c,VIP_Type__c
                                    FROM VIP_Type__c
                                    WHERE Contact__c in:contIds];

    Map<Id,set<string>> existingTypeMap = new Map<Id,set<string>>();

    for (VIP_Type__c type: vipRecs)
    {
        map<string> existingTypes = new set<string>();
        if(existingTypeMap.contains(type.contact__c))
        {
            existingTypes = existingTypeMap.get(type.contact__c);
        }
        existingTypes.add(type.VIP_Type__c);
        existingTypeMap.put(type.contact__c,existingTypes);
    }



    for (VIP_Type__c type : trigger.new)
    {
        if (existingTypeMap.contains(type.contact__c))
        {
            if (existingTypeMap.get(type.contact__c).contains(type.VIP_Type__c))
            {
                trigger.newMap.get(type.Id).addError('This Type already exists for this Contact');
            }
            else
            {
                map<string> existingTypes = existingTypeMap.get(type.contact__c);
                existingTypes.add(type.VIP_Type__c);
                existingTypeMap.put(type.contact__c,existingTypes);
            }

        }
    }
    
// Query the Accounts
		List<Account> acct = new List<Account>();

// Use the VIP Types to get all the related Types for the Account 
			acct = [SELECT Id, VIP_Types__c,(Select VIP_Type__c FROM VIP_Types__r) 
					FROM Account 
					WHERE Id in :acctIds]; 

// Iterate over each Account and VIP record 
			for(Account a : acct){ 
				a.VIP_Types__c = ''; 

				for(VIP_Type__c vip: a.VIP_Types__r){ 

					if(!a.VIP_Types__c.contains(vip.VIP_Type__c) || a.VIP_Types__c == ''){ // Check if the Type is already in the Account Field. if not add it otherwise skip 

					a.VIP_Types__c += vip.VIP_Type__c + '; '; 
					} 
				} 
			} 
// Update the Account 
		update acct; 
}