I am running my own mailserver for several years now and it is quite possible. The problem is, that your IP is new to the other MTAs and you need a couple of months to build up the reputation. Services like the one from Microsoft have forms, where you can delist yourself from their blacklists. Even though you are not blacklisted, it helps for the reputation if you fill out the forms with the MTAs you have problems wi…
Yes, I think this is a great part of the problem. My IP doesn't have any reputation. But how do I build one? I send a very small volume of emails, I'm just one person.
Eventually though, gmail will typically accept email from home IP addresses. Google apps for business seems to be even trickier than that: they have an opt-in strict setting which blacklists (outright rejects) anything remotely suspicious. It'll tell you where you stand through delivery failures, but it also means you'll end up having to call whomever you're trying to reach.