if your threat model were 'encrypt everything at rest', invitations to people outside your own service would be tricky as they have to be machine-readable text in a specific format. i'm sure it's possible but you'd have to be specific in looking for that as a feature.

my needs are more modest - don't store email in GAFAM or particular regimes - and i use runbox, which is bog-standard except for being stored somewhere else, being paid, and having slightly more homely webapps. using 'evolution' on linux, a bog-standard email program that's also a bit more homely than alternatives, invitations go out to whomever i choose and look normal. i make recurring events for myself all the time and remove individual occurrences. i've added on ical subscriptions for things like country holidays, which are the first thing you'll notice missing when you leave outlook.

the mail's just imap and the calendar's just caldav. when you get into providers that don't provide imap or caldav for (valid) security reasons, that's when you're more likely to get integration issues with regular people.