I wonder what you mean by the phrase: "Outlook is ITAR compliant". I could not find any statement from Microsoft to that effect.

See https://www.virtru.com/blog/itar-compliance/ and http://www.interlink.com/blog/entry/is-office-365-international-traffic-in-arms-regulations-itar-compliant

I've read that there is a special International Traffic in Arms Regulations (ITAR) compliant version of Microsoft's Office 365. It supposedly starts at 30K users and is expensive.

Supposedly "ITAR compliance starts with registering with the Directorate of Defense Trade Controls (DDTC) and paying a registration fee." I doubt Mozilla has done that since they don't sell the software.

However its not clear to me that Microsoft has done that for Outlook. Perhaps you assuming Outlook is ITAR compliant because it is mentioned in articles about ITAR such as https://support.microsoft.com/en-us/help/2553469/how-to-export-an-exchange-mailbox-by-using-outlook-in-the-context-of-deployments-of-office-365-in-dedicated-and-itar-environments

You need to talk to a ITAR expert.

MS Office 365 is an entirely different story. The reason why an ITAR compliant version of Office 365 is needed is its cloud nature. Standard Office 365 cannot guarantee that the data you use it on remains under U.S. legislation. Thunderbird stores its data locally or in the configured mail account(s). So if the mail accounts you have configured are ITAR compliant then Thunderbird is ITAR compliant too.