The short answer would be to store them all in the refrigerator once opened. The named condiments can all last for months (always check the label and try not to exceed a use-by date!) if stored properly.
Back in the day the recipe for ketchup, mustard and others was different and most importantly was higher in salt. Salt is a natural preservative and can protect against pathogens. However, with the established link of high salt content and hypertension, many food manufacturers gradually decreased the salt content of food products (and yes, if you ever wondered, french fries at McDonald's tasted differently 10 years ago!).
Other preservatives (e.g. Sodium benzoate) were also dropped by the food industry and ceased to be used. Overall it means that the ketchup we use today contains much less 'nasty' stuff than it used to and much more susceptible to the microorganism action. All the additives, used in the production of foodstuffs are only used when absolutely necessary (and the manufacturer should justify its use).
In the situation where you are unable to store condiments in the fridge or need to have them on the table for a prolonged, always take the precautions against microorganism growth. Ensure, that the lid is closed tightly after use, use clean utensils and avoid contamination. If some of the product left on the cap, clean it, before putting it back to fridge.
Hope that helps :)