Instagram Embeds - you have to add the HTML?

Not all email clients support showing iframe embeds. You can find a list of some that do and don’t here, although it might be out of date by now:

One option would to show different content in email vs the web to make sure you have content that works in email. Ghost already has an email-only card for that.

You could vote the opposite feature: To support an “html only” card:

With both of these cards available, you could display the iframe on the web and something else in email.

You could also vote for this idea that sounds like exactly what you want: A special Instagram integration that takes care of making it work in email and on the web for you:

Since Ghost is open source, you could also consider creating something like that yourself, or funding someone else to work on it.