So apparently IFTTT strips certain HTML tags when you save a WordPress recipe, most notably the iframe tags, so if you’re looking to use the code snippet provided by Instagram, etc. to embed your content from there, it won’t work. Even if it did, if you use a responsive layout the iframes will break the layout of the site, unless you have a hacky method in place to bypass that limitation. I’ve also experimented with using bare links and relying on oembeds to pull in the content, but it doesn’t generate a thumbnail image that I can use when sharing my post to networks like Twitter and Facebook. Bah.
So the best thing for now (at least where Instagram is concerned), is to use the source url of the photos and videos rather than relying on any degree of embedding automation to ensure I can display my images correctly (and WordPress can properly generate thumbnails for them). For Instagram videos I use a thumbnail image that will link readers to the video on Instagram. Best solution I can come up with for now.