How can I hide calendars from Siri?

Short answer: No.

No, at this moment it is not possible to hide calendars from Siri. I highly recommend you send this feedback to Apple.

A workaround would be to use a second calendar app to show the calendars of your family and use the normal calendar app only for your own calendars.

Siri seems to show exactly those events, which are in one of the enabled calendars in the calendar app from apple. So if a calendar is not visible in the app, its not visible to siri either and vice versa.

If you use a second calendar app as your daily driver, you can therefore use the following workaround.

• Setup the calendars in apples calendar app, the way you want Siri to use them.
• Activate different calendars in your third party calendar app as needed.