Came across this post today and yes, its pretty hard to convince people that Anime is just childish cartoons because we all know, Anime is catered for both children and adults. They are simply looking in the wrong places.
The best places to look for mature looking anime is looking for shows in the Seinen or Josei demographics. These shows are praised for its realism, maturity and its drama with a few exceptions. Here are some shows to look out for that don’t contain any or little ecchi (on top of my head):
Honey and Clover
5 Centimeters Per Second
Also, don’t give up! If they are still unconvinced, you can’t say that you haven’t tried.