To clarify, you're looking for all issues (which represent users) who don't have a birthday today - so a JQL for day and month which ignores year (given that year could be anything in a 100 year spread)?
This isn't something which is possible with base JQL, as it searches for specific dates - eg. startofDay() assumes that is today in 2019, not today in any year.
You'd need to consider a scripted field or similar which can identify if today is a user's birthday using the day and month. An app like ScriptRunner should allow you to do this. I'm not so hot on ScriptRunner Cloud though so best to read through the vendor's support page or contact them directly with that question!
A simple alternative is to set their birthday each year to the actual date - for example:
More manual, but a simpler fix.
Let me know if this was not the issue or the field isn't on an issue-level but a user-level.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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