I use a debit card for online purchases. I’ve had no problem disputing charges in the past. Most debit cards offer the same protections as credit. When my card number was stolen by a skimmer at a restaurant, they refunded me all of the money and apprehended the teen responsible for the fraud.
Banks take card fraud very seriously. I work for a CUSO with an enormous fraud department, and regardless if it’s debit or credit, they treat transactions the same.
Credit unions in general have pretty good service, I think.
I wouldn’t want to use a debit card online.