I'm trying to remember how this works. Are they added by Google irrespective of an ad code placement?
If they rely on an ad code in the xenForo advertising system then it is easy enough to hide that code from logged in users with the ad position settings:
User is NOT a member of any of the selected user groups: registered, and hide on mobiles with CSS in extra.less by wrapping it in a div with class
e.g.
<div class ="nomobile">AD_CODE </div>
and in extra.less
Code:
@media (max-width: @xf-responsiveMedium)
{.nomobile
{
display:none
}}