Hi folks - Coda developer here. I was able to reproduce the issue and on the surface, this looks like a bug in Obsidian to me. Happy to be proven wrong, though 
When a Coda doc is normally rendered, we limit the ability to embed the doc for security by specifying a Content Security Policy rule: frameAncestors: 'self' *.coda.io. This tells browsers to limit iFramed versions of the content to be from pages served within the origin domain (coda.io) and subdomains of coda.io, but no other sources.
However, we have a special form of the document we allow to be iframe embedded, available from the embed panel in the sharing dialog. This URL is of the form https://coda.io/embed/<docId>. When that URL is requested, we append a * to the CSP rule, enabling this document to be iFrame embedded by any site. The CSP rule here looks like: frameAncestors: 'self' *.coda.io *.
My guess, without knowing too much about how Obsidian works under the covers, is that it is intercepting the browser-based load & render of the iframe, causing its embedded copy of Chrome to believe the page is coming from local content using something like a data: URL which is outside the scope of the * rule. If true, I would expect any service’s embed URL that uses the frameAncestors CSP rule to similarly fail to render within Obsidian.
Regardless, if an Obsidian developer would like to reach out, I’m happy to chat offline and figure out a solution.