Create list of values to check for multi picklist

       Set<String> typeSet = new Set<String>();
       String allStr = 'All';
       typeSet.add('\''+ allStr + '\'');
       for (Financial_Goal__c goal  : Contact.FinancialGoals__r){
         typeSet.add('\''+ goal.Type__c + '\'');
       }

Query using INCLUDES and using String.join to create string of List.

List<Content__c> typeMappings = (List<Content__c>) Database.query(
contentMappingQueryFactory.setCondition('Status__c=\'Publish\'
AND Id!=:featureMappingId AND (Goal_Type_Attribute__c INCLUDES(' + String.join(goalTypeList, ',')+ ') 
AND Age_Attribute__c INCLUDES(' + String.join(ageList, ',')+ ') 
AND Employment_Attribute__c IN :employementList AND Gender_Attribute__c IN :genderList 
AND Net_Worth_Attribute__c IN :netWorthList)').setLimit(2).toSOQL());

Use , for OR and ; for AND to match values in picklist

OR:
will match for any value in picklist
String.join(goalTypeList, ',')

AND:
will match for all the value in picklist
String.join(goalTypeList, ';')