Emails being accepted by large organisation

Yes. Even if senders and sender domains are added to safe list, if emails are detected as Malware or High confidence phish ,they will be blocked. But since this is happening for a single organization and not all emails to recipient are getting blocked this is possibly because of some security policies blocking for example any particular Attachment extensions, URL/URL domains, IPs etc. Best way to figure out will be contacting recipient organization's IT team since you are not receiving NDRs.

As you mentioned emails go through once communication is established. This happens when O365 mailbox intelligence blocks emails for Impersonation or Spoof protections. In these cases it is best recommended to set up your SPF, DKIM and DMARC authentications accurately.