shadowtanuki: offers a practical suggestion (take responsibility for what you see on chess.com, because you know what the mod limitations are)
everyone else: doesn't want to hear it
It's a raccoon fight! Fight! Fight! Fight!
Okay, so the default becomes you have to click something to see images. Are you going to stop being mad if someone posts images that are bad? And if someone else is looking at the screen you're on, and they see a lot of dark or blurred out images, what kind of website are they going to think you're on? I think we all know now when and where there's likely to be graphic images on this website. Maybe, as some people have suggested, you should just stop using it if you don't like what you see here.
... And if someone else is looking at the screen you're on, and they see a lot of dark or blurred out images, what kind of website are they going to think you're on? ...
It's not dark or blurred out. It just doesn't show until you click on the eye icon. Perhaps you're just not familiar with this feature in messages.
I've been here 10 yrs and I'm not familiar with THAT feature. Come to think of it, I'm not familiar with a lot of things. 
I think this feature only works on the website. On the app, he’s sent me pictures that were not hidden.
... And if someone else is looking at the screen you're on, and they see a lot of dark or blurred out images, what kind of website are they going to think you're on? ...
It's not dark or blurred out. It just doesn't show until you click on the eye icon. Perhaps you're just not familiar with this feature in messages.
You're right about that, I thought it showed a dark square where the image was until you clicked the eye icon, but it says "Text and images are not displayed," or something to that effect.
... You can scroll the screen so you don't have to look at it.
Too much hassle. You don't want it to show by default after you've been offended by it once. Besides you may not be the only one looking at your screen.