It's usually the other way around, in my experience: I'm sending something from a relatively small provider (or a institutional mailserver), and it's rejected (sometimes silently) by a larger receiver. The reasons tend to be opaque, and support is nonexistent (presumably because the overwhelmingly amount incoming mail is illegitimate).
It's a hard problem, and the reality is that Google has made the average user's email experience radically better. But the drawback of that is that they rule the ecosystem by fiat, and that there are relatively few entities that can play keep-up with Google's (unpublished?) standards for reliable delivery. Getting booted out of Gmail increasingly means being left out in the cold, especially as institutions (like the company I work for!) use GSuite for mail.
If you're paying for your email provider, I would think opening up a ticket and asking to let their email through would not be much of an issue, if this ever happens.