What does that even mean? Fastmail is mostly or entirely FOSS on the mail backend but the web front end is currently non-FOSS. You can of course use a FOSS client instead.

Hosted services are more about hosting than about the backend software anyway. You can use something like mailcow to self-host email if you don't mind headaches.

mxroute.com is probably all FOSS but they don't make an issue of it. Actually idk what web control panel they use now. It was formerly cpanel but they switched, probably for cost reasons. The webmail ui's are roundcube and a few others.