When plugin is deactivated, styling goes crazy

On the wordpress site I am working on, there is a Facebook “Like” plugin currently active (version 1.9.5). For some reason, when I deactivate the plugin, all of the styling of the posts goes haywire, with images overlapping each other, text overlapping images, etc.
However, as soon as I reactivate this plugin, everything goes back to normal.
I tried doing a hard re-load of the CSS and that didn’t help.
Why is this happening? How can I deactivate this plugin without affecting the whole layout of the site?

Here’s the URL: https://nylonmag.com/nylonblogs/