Personally I do use the MF liquid detergent. (Bought a gallon of the DP)
I copy/pasted the following from one of the articles I linked above...
This is courtesy of Mike Phillips
Washing and Drying
Another question that comes up all the time is how to properly wash and dry microfiber polishing cloths. It's best to keep this process simple and uncomplicated.
Washing
Wash your microfiber polishing cloths in the warm or hot temperature setting with a quality detergent on the normal or heavy duty setting. Choose between these options by how dirty your microfiber polishing cloths are; if they are really dirty with lots of polish and wax residue then use the hot temperature setting, on the heavy duty wash cycle. If your washer has an optional secondary or extra rinse cycle you can use this option to insure all the detergent is rinsed out before drying.
Liquid or Powder Wash Detergents
There are people that will argue that only a liquid detergent should be used for washing microfiber polishing cloths to reduce the potential for any undissolved powder particles to somehow attach to the nap of the microfiber cloth and remain their, (undissolved), through both the wash cycle and the drying cycle. Personally I've never had a problem using powder style washing detergent. The polish and wax used on this truck was wiped off using microfiber polishing cloths washed using Tide Powder Detergent.
Here's a tip... <-- Important
When using a powder type laundry detergent. Before you add your microfiber polishing cloths, first start by filling the wash tub with water and then add your laundry soap, (both powder or liquid), and let the laundry detergent fully mix with the water to create a uniform soapy water solution to then add your polishing cloths. With a powder type laundry detergent, the violent mixing action by the agitator will allow the powder particles to fully dissolve, thus used correctly a powder type laundry detergent is a liquid.
If you add your polishing cloths first, then pour the powdered laundry detergent on top of them and then start the load, the powder particles will have to work they're way through all the polishing cloths in order to mix and dissolve in the water. So create your soapy detergent solution first and then add your polishing cloths.