Baby detergent?

Dana • baby #1 born May 2016, baby #2 due February 2019
I washed some of the baby's clothes, but the last time I spoke with my mom, she said I should have used dreft. I normally just use regular tide. Is it really that big of a deal? I'm assuming it depends on the baby and how sensitive their skin is, but how common is a reaction to regular detergent?
Thanks in advance!!