When browsing a site in IE Mode, if a user clicks a link to go to a modern website, and that website requires a client certificate (basically any *.mil site using smart cards), the site will not load and the tab will just wait with a spinning throbber. I believe this is because the Chromium certificate selection UI is hidden when browsing in IE mode.
If the site was already navigated to that the client certificate was previously selected in a different tab, then the page navigation will work correctly. Another workaround is right-clicking the link and selecting Open link in new tab. This is not an issue when starting navigation in a new tab or the full IE browser; it's only a problem with IE Mode tabs.
This is especially problematic for my organization as our homepage is based on SharePoint 2013 where there's several workflows that require IE mode. Any links from our homepage to cert-required modern sites fail to open.