How to use GetSObject to retrieve related data in a null safe manner?

You need to add a null check. The only reason this would fail is if your parent record is null. One option may be to just get the value statically:

String text = record.Parent__r.TextField__c;

If you cannot use a static reference, I recommend a cross object getter like I shared here. First create this top-level class:

public with sharing class CrossObject
    public static Object get(SObject record, String field)
        if (record == null) return null;
        if (!field.contains('.')) return record.get(field);
        return get(

Then instead of:

String text = (String)record.get('Parent__r').get('TextField__c');

You could use:

String text = (String)CrossObject.get(record, 'Parent__r.TextField__c');