As far as I can see, if you load the form then it always throws the message, you can see that happens if you load the page up without an iframe and go straight to the url.
Best idea I can think of is that you put the url of the form in a data attribute rather than the src of the iframe, eg looking something like this:
<iframe id="googleMemberForm" data-src="https://docs.google.com/forms/d/e/1FAIpQLSfMDHgqXiUrk2400dLslI2HySfxF1h-cFB3VFClm4D8-oRGfQ/viewform?embedded=true"></iframe>
The in the same js handler that shows the form now you add an extra bit of js that does this:
So the code that shows the form modal will also load the iframe too.
You'll still get the warning after you've loaded it but hopefully that won't affect normal users browsing the site, until they've at least clicked the get started button to load the form.