Example post: https://simplepaymentwidgets.mystagingwebsite.com/2018/07/ig/
Embedded instagram post
Empty container
Console error: Refused to display 'https://www.instagram.com/p/BlMg3iolq9e/?utm_source=ig_embedembed/captioned/?cr=1&v=9&wp=1044&rd=simplepaymentwidgets.mystagingwebsite.com#%7B%22ci%22%3A0%2C%22os%22%3A975.6000000052154%7D' in a frame because it set 'X-Frame-Options' to 'sameorigin'.
Reproducible on WordPress.com simple, Atomic and P2 sites.
Also happening on support page: https://en.support.wordpress.com/instagram/instagram-images/
Instagram Widget is still working as expected
I was able to repeat on a WordPress.com test site (same shortcode handling for PHP and JS as Jetpack)
Editor:

Front-end: https://selawidgettest.wordpress.com/2018/07/31/insta-test-for-al/

I've tried Instagram API developer channels and this is the only place I could publicly log a bug: https://developers.facebook.com/support/bugs/534047397026536/?disable_redirect=0
I've worked out the problem -
the current iFrame we show is something like this:
<iframe class="instagram-media instagram-media-rendered" id="instagram-embed-0" src="https://www.instagram.com/p/BkuuaBeDUGj/?utm_source=ig_embedembed/captioned/?cr=1&v=9&wp=1316&rd=juiced.blog#%7B%22ci%22%3A0%2C%22os%22%3A1235.7000000192784%7D" allowtransparency="true" frameborder="0" height="795" data-instgrm-payload-id="instagram-media-payload-0" scrolling="no" style="background: white; max-width: 658px; width: calc(100% - 2px); border-radius: 3px; border: 1px solid rgb(219, 219, 219); box-shadow: none; display: block; margin: 0px 0px 12px; min-width: 326px; padding: 0px;"></iframe>
we need to make sure we add an/embed to the URL for it to show:
<iframe class="instagram-media instagram-media-rendered" id="instagram-embed-0" src="https://www.instagram.com/p/BkuuaBeDUGj/embed?utm_source=ig_embedembed/captioned/?cr=1&v=9&wp=1316&rd=juiced.blog#%7B%22ci%22%3A0%2C%22os%22%3A1235.7000000192784%7D" allowtransparency="true" frameborder="0" height="795" data-instgrm-payload-id="instagram-media-payload-0" scrolling="no" style="background: white; max-width: 658px; width: calc(100% - 2px); border-radius: 3px; border: 1px solid rgb(219, 219, 219); box-shadow: none; display: block; margin: 0px 0px 12px; min-width: 326px; padding: 0px;"></iframe>
When I change this in the browser DOM it works:

I just need to work out how to change Jetpack or WP.com to change the embed url to append embedto the URLs now 馃
Actually, this is a problem in core WordPress as well as that supports the Instagram oEmbeds: https://core.trac.wordpress.org/ticket/44688#ticket
Another case reported in #5132444-hc
Also #5129765-hc
From @pento on Core:
This is caused by Instagram.
Their oEmbed response has added ?utm_source=ig_embed to the URL, which the JavaScript they use to generate the iframe doesn't allow for, hence embed/ appearing after that URL parameter in the iframe src, rather than before. Until they remove the URL param, or update their JS to allow for it, Instagram embeds are going to be broken.
Unfortunately, there's not a lot we can do about this, Instagram have broken embeds for everyone, not just WordPress:
https://twitter.com/search?f=tweets&vertical=default&q=instagram%20embed&qf=off
This seems to have been fixed by Instagram now - closing
Most helpful comment
This seems to have been fixed by Instagram now - closing