Birthdays in Contacts
On my iMac in Contacts Birthdays are grayed out and can't be edited
iMac 27″, macOS 10.15
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you have not told us what steps you've tried, but:
when you click "edit" the birthday field is shown greyed out.
you then click the "+" sign and choose "birthday"
when you do that, the birthday entry will then be editable.
have fun.