How to not show birthdays from Contacts on Apple Watch?
Contacts.app in macOS 11 Big Sur (and the underlaying iCloud) now offers more differentiated date fields which address use cases like yours and more.
Preparation:

Open Contacts.app &gt; Preferences &gt; Template.
Add fields &gt; Dates: Birthday or custom (depending on what's in your template already)


Locate the date section in the template.
Leave the original &quot;birthday&quot; field.
Add a custom field &quot;birth-day&quot; or similarly odd spelled to never collide or get confused with the real &quot;birthday&quot; field.
You may also add &quot;date-of-death&quot; if you want to document your deceased contacts.

Then for any contact do the following:

Fill the real &quot;birthday&quot; field if you want the person to show up in the dedicated &quot;Birthday Calendar&quot;.
Fill &quot;birth-day&quot; (your custom date field) if you want to have that documented for a contact but not show up in the dedicated &quot;Birthday Calendar&quot;.
This should also propagate to your Apple Watch then eventually.