I got married in 2020, so I filed my 2019 taxes as single. But my husband (as of 2020) accidentally filed as "married filing separately" even though we weren't married in 2019. I tried e-filing and it was rejected saying that my husband already claimed me as a dependent - even though he did file separately - but married. Now how can I complete my tax returns. Should I put "married filing separately" even though we weren't married last year?
No. Do not put married filing separately. If you were not married in 2019 you cannot file as married. Your spouse messed up and he should amend his return when it has been fully processed. Guess he did not realize that getting married in 2020 did not mean filing married for a 2019 return.
Since he has used your SSN on his return somehow, you cannot e-file now. Your own return on which you file as Single, will have to be printed, signed and mailed. You will not be able to e-file this year, even if he amends, since amending takes many months.
And...by the way...next year when you can file your 2020 return as married filing jointly or married filing separately, you need to understand the difference between filing MFS or MFJ. Married filing jointly is almost always better.
https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately
https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states
Best Wishes!