As long as you use the birthdate that is on file with social security, you should not experience any rejections. The social security database must match birthday on file for the federal return to be accepted. For the New York matching, it's an entirely separate program and it looks for the driver's license info that you input which includes the license number, issue/expiration date and in NY the "document ID". It doesn't ask for the birthdate.
Things do change from time to time, but should you get a rejection on the state it would be after federal is filed so you could change the year then and resubmit.
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