The problem with all these new TLDs is that spammers have poisoned the well. The overwhelming majority of the spam I get comes from .club, .xyz, and other "gold rush" TLDs, so I can't be surprised if some organizations just reject them outright.
Makes a good case for expensive TLDs
Sounds like a problem for their IT.
Clearly; but that doesn't fix the situation, only makes it worse. Now you have two problems: your client cant receive your emails and they're the ones who have to fix it.