The simple answer is no. Don't use Fabric Softener (liquid or dryer sheets) on any clothing that has a polyester or spandex blend. It can cause spots on the clothing.
For maximum product life of your clothing and to set the fabric dye simply add 1/2 cup of white vinegar to your wash. Adding the vinegar will prevent colors from fading, and give you a natural fabric softener. The vinegar smell goes away in the wash.
The best all-natural fabric softener is generally made by mixing one liter of distilled white vinegar with around 10 drops of essential oil.
Another option for baby's clothes is baking soda. All you need is a little baking soda added in during the rinse cycle and your good to go. It’s simple and it works great.
All baby's are different, some baby's are more sensitive than others. Fabric softener is not suitable for all young children, The majority of fabric softener products tend to use harsh chemicals that can irritate you baby's skin.
For Best Results:
Machine Wash - Cold Water - Gentle Cycle - Wash Inside Out - Do Not Soak - No Bleach - Use Non-Chlorine Bleach Detergent - Hang to Dry - Or Dry On Lowest Heat- Over Drying will Fade Colors