My (cis female) birth certificate erroneously was filled out with "male". Same error happened on the birth certificate of my mother (who is also cis female). It's never caused either of us any problems. Schools enrolled us as female, driver's licenses say female, etc.

When I was in college in the early 2000s, my dad's mother helped me get a copy of my birth certificate, and was horrified her beautiful granddaughter was listed as male. She called up the county clerk and raised Cain, and then informed me it had been corrected. I've never needed to get a fresh copy since then, so I don't know for sure, but it sounded like the word of an angry old lady was enough to get an update filed.