Facebook will not grab images from my website

Perhaps you have to set up Open Graph meta.
You can try WP Facebook Open Graph protocol or another OG plugin.

But it worked before. And I can copy-paste URLs from any random website and it will find images to display. It only doesn’t work with mine.

Here’s a link to my Facebook page, where it worked as late as June 10.

https://www.facebook.com/pages/Truths-for-Tots/325514794198936

You use Yoast WordPress SEO plugin. It adds OG meta tags, og:image also. So, deactivate the WP Facebook Open Graph protocol plugin to avoid tags duplication.
Actually FB din’t catch the image meta. Try to debug
https://developers.facebook.com/tools/debug

BTW google analytics code also duplicated (in header and footer).

Thank you so much. That fixed it.