Okay, this was working fine a few versions ago (2.?) but now it is not.
I am running Version 18.104.22.168 and have two custom types, one with a custom taxonomy. I was just trying to add a new post and the form for the taxonomy showed up on the New Post page. I think it also prevented the front end from seeing the entry. I looked at the new page for the other custom type and the taxonomy fields were there, also. At least they weren't there for the New Page page.