Hi, Thomas.
I believe you’re requesting the same thing as one of our existing feature requests: https://tribe.uservoice.com/forums/195723-feature-ideas/suggestions/5678413-embed-calendar-on-other-web-sites
Please do add your vote there.
This allows us to gauge interest in this particular feature request, which helps us prioritize our development efforts.
My personal idea for this would be to add a query parameter to the URL, like http://wpshindig.com/events/?iframe=1, and if that is true, then you could not load the site’s header, sidebar, and footer. This could be via CSS or maybe via PHP.
However, the iframe size may still be an issue when a visitor clicks from the full Month View into an Event Single view… but maybe an iframe buster could be used so that all links open in a new window (although that may not be ideal for all use cases).
Anyway, if you want to move in that direction yourself instead of waiting for the possibility for that feature request to be released (if ever), you may want to ask your developer or reference our documentation and list of known customizers.
I hope this information helps. Please let me know if you have any follow-up questions on this topic.