I wonder if that's a big red flag or a little one. Either way, we should all be open to constructive criticism. After all, sometimes someone will see something that we don't. However, criticism, when it is constant and/or belittling can mean abuse and that is a big red flag.
I think this is a really good point, Jennifer! What kind of criticism are we talking here? No one responds well to abusive criticism, but being able to accept constructive criticism is an essential life skill.
If someone said they didn't accept criticism well, I would want to know what kind. If it's the abusive kind, I would think they were perfectly normal. If they said they couldn't accept constructive criticism, I would consider that a concern. If they fly off the handle when they interpret someone as criticizing them, I would consider that a red flag.