I recently did this with CSS on the profile page.

I don’t think there’s a way to do it on the actual posts (both past and going forward). So step one would be to audit who has a signature and then manually remove all the existing signatures from profiles. 

Then here’s the css I figured out (i’m not the best so it could be off; in fact, I recently noticed the header for it was visible again, though the ability to see/edit the field itself was still hidden)

/*start-- hide SIGNATURE field on Edit profile settings */
#customcss #root
div.box.box__pad.box__unmar.userprofile-personal.qa-user-profile-box > div > div.user_data.flag__body > div > div:nth-child(1) {
  display: none;
}
#ProfileSettingsForm_signature
{
  display: none;
}
/*end hide signature */

If you work out any tweaks to this in your implementation, please share so I can update mine (it’s on my list, but not something I’ll get to soon.)

Hey ​@DannyPancratz 

Where as I have the opposite. I have removed from the posts easily enough in the Style section.

/* CSS to remove USER SIGNATURE from posts */

.signature{
  display: none;
}

But there appeared to be a table in the ACTUAL user profile. Viewing mode rather than edit mode.