When I ran my own mail server, I was lucky to even make it to the gmail spam folder. More often it didn't even make it that far. From what I can tell, O365 is even worse though.
replyThey should go through, at least to spam - but your setup needs to be flawless, meaning you need to correctly set up the 'holy trinity' SPF, DKIM, and DMARC.
replySites like mail-tester.com, learndmarc.com, or sending a mail to ping@tools.mxtoolbox.com (which will reply a report to you) are pretty useful for that.
But yeah I have only limited experience I suppose. Having some mail correspondence with friends in the hopes of improving my domain's reputation to those mail servers.
Oh and btw, I relay through my cloud providers mail delivery system - doing it from your own IP is probably a whole different league.
I run my own email server on own ip since 2005. Never had any issues with gmail or M$. Changed IP at least one time, no difference from the first day on.
Just one time I had to activate SSL for inter server communication. But that was a known thing that gmail was rejecting you otherwise.
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