Currently, I use microfiber detergent for my "nice" or "good" microfiber towels, but I use " free and clear" detergents, which you can find at any grocery store (it's made for people with allergies) for my general use microfibers.
Honestly, I know a lot of people who just use regular, free & clear detergent for all of their microfibers and have yet to have any negative effects. I always do an extra rinse to ensure it's free of any and all detergent. I also hang dry my super expensive ones and dry on low the others, but again, others just dry their towels (not in high though) and their towels are fine.
You can get as intense or basic as you want. Generally, don't dry on high, and follow the directions and you'll be fine. Happy detailing!