Hmm, I’m currently using a me TLD and I don't think I’m having trouble. But I’m on a good host and all my dmarc etc is set right. Give yourself a check with https://www.learndmarc.com/
Yeah, I have SPF, DKIM, and a strict DMARC policy all configured for Fastmail, but some hosts just refuse to pass the mail. It's pretty random and sporadic, but it happens. I've also had some web forms refuse to recognize it as a valid email address.
A long time ago my fastmail.us didn't get accepted in places but I can't say I've had problems with that in recent years. Never had a issue with my me, I think people are well aware of the new tlds now.
As an extra bit of authenticity I've been smime signing my sent mail. Not encrypting, just signed. I figure that something no spamer is going to do and I’m hoping any spam filter will look at and pass it. Assuming they don't ignore it and make it a waste of time.