The web standards leave quite a bit up to the implementation. Support for scripting is completely optional, for example; a compliant browser is not obligated to load or run your JavaScript. Or to render images, for that matter—the standards do not exclude screen readers. If your site is unusable when scripts are disabled it's your site which is non-compliant, not the user agent. On general robustness grounds you would do well to ensure that your site continues to operate properly even when third-party resources are unavailable, including Google Analytics. After all, the script could fail to load because the server is down and not because it's being blocked by an extension.

Certainly it's not a bug (on your part) that the user agent rendered the page as the user directed, but that isn't the actual complaint. The issue is that the page is over-complicated and fragile, proving unfit for purpose when faced with the slightest deviation from the default behavior of the top two or three most popular web browsers.