First, lets identify the field you want to hide.  It's a bit technical but an amazing trick to finding what you need.

Open up your browser of choice (they all support this now, but may need to be enabled - google "browser name" inspect menu).  Find the element you want to hide and right click it then click on inspect.

You will now see the code open up where you can then hover over the code to see it highlight the element on the site.

If you look at the class="" you will find a common name membership_birthdate.  You can now target all items with this line:

.membership_birthdate { display: none !important; }

Take this code and add it to your page layout.  On refresh this field will no longer be visible. 

Keep in mind, if you do this for a required field, you will need to use some Javascript to fill that field with a default value.

$("#content_last_name").val("doe");