[SalesForce] Can an ID in a lookup field ever be invalid? Anywhere

I want to avoid using ActionRegion because it forces the user to enter data in required fields in other parts of the page form.

One of the main uses of the apex:actionRegion tag is to do the opposite of this, by sending only the elements that are children of the actionRegion with the request to the server. The visualforce parser will only enforce required validations on fields that are included in the request, and thus you can strategically place an actionRegion to get around unwanted validation.

In this case of the code in your question, the apex:actionRegion tag is just wrapping the wrong elements. Change it so the actionRegion only wraps the inputField.

<apex:actionRegion>
     <apex:inputField value="{!contact.AccountId}">
        <apex:actionSupport event="onchange" action="{!AccountPopulated}" rerender="accinfo, msgs"/> 
     </apex:inputField>
</apex:actionRegion>

You can do something like this. Basically you would need to get the opportunities of all the records that you're inserting / updating, get the associated accounts and then set the account values in the customOject's account__c field.

trigger autoPopulateTrigger on customObject__c (before insert, before update){

    //get the oppotyunity Id's and store it in a set.
    set<Id> opptyIdSet = new set<Id>();
    for(customObject__c co: trigger.new){
        if(co.opportuntiy__c != null){
            opptyIdSet.add(co.opportunity__c);
        }
    }

    //query the opportunity records and get the associated accounts.
    map<id, opportunity> opptyMap = new map<id, opportunity>{[SELECT id, accountid from opportunity where Id IN: opptyIdSet]};

    //update the account value based on the opportunity in the record.
    for(customObject__c co: trigger.new){
        if(opptyMap.containsKey(co.opportunity__c)){
            co.Account__c = opptyMap.get(co.opportunity__c).accountId;
        }       
    }

}