Are your domains set up correctly? That sounds suspiciously like something isn't set up correctly and their client's thought it was spam.
I use an @fastmail domain. The issue was how they handle RSVPs when your default calendar is an external one. RSVPing from within Fastmail attempted to Accept as my old Gmail address, who wasn't invited to the interview. On the interviewers end it looked like I didn't respond.
In some contexts, fastmail is viewed as a "throwaway" email provider. I ran into this when I was trying to provision a couple of VMs at a hosting provider. My fastmail email address was rejected. After contacting their support, they said they did not accept "throwaway" email addresses. I had to use a gmail acccount. The irony did not seem apparent to them.
My only scare with not using gmail and outlook calendars. However I moved to Zoho for mails and nextcloud self hosted for calendars. For mail delivery I make sure to verify again n again my SPF DKIM is valid or not but it’s a scare still :(
Isn’t it so bad that it’s overly hard to move away :(