The "IE Tab" add-ons offer some convenience, but I don't know that their authors can support applications like Outlook Web Access/App (how many people still have accounts on older versions of Exchange?). Did you try the support link on that extension's page on the Add-ons site?

Since email is a sensitive application -- personal/confidential information flows through it, and losing mail is a disaster -- I recommend using the site in IE 11. If it's your only use for IE, you can make it your IE home page for fastest access.

2007 Outlook Web Access was installed when we got internet and the ability to create distribution lists was available then. Don't know what happened that it's not now. Confused that we have to switch to explorer or install Internet Explorer tab to get it to work. Also don't know what other email to use to communicate with church members (as a group).

It is normal to get the "Light" version of OWA 2007 in browsers other than Internet Explorer.

If you are also getting that in IE, I saw a tip to add the OWA site to your list of compatibility mode sites in IE. That might also fix the problem in IE Tab but I can't test it myself.

See the "Workaround" section of this article: https://support.microsoft.com/kb/2866064

The "IE Tab" extensions for Firefox is not a emulator as it uses the IE installed on Windows in a Firefox tab. You may as well use IE when you need it anyways.