Hi @Mojmir Kavan,
Thank you for posting to Microsoft Community.
Based on your description, I want to confirm if your issue is that some emails sent from the internet through your on-premises Exchange to O365 users being delivered but marked as non-accepted domain.
If so, I want to share the following with you.
Please make sure you have the proper DNS records set up for O365 to verify your on-premises.
Please double check you have configured the accepted domain in EAC correctly.
You could refer to Manage accepted domains in Exchange Online | Microsoft Learn for more information.
It could be the most likely reason, since Microsoft defined "non-accepted domains" as:
The Non-accepted domain report in the new Exchange admin center (new EAC) displays information about messages from your on-premises email organization where the sender's domain isn't configured as an accepted domain in your Microsoft 365 organization.
For more information, please refer to Non-accepted domain report in the new EAC in Exchange Online | Microsoft Learn.
Also, are these subdomain email addresses? You have to add these in as additional domains in most cases. Please remember also have to add in .com, .net, .info…separately.
Hope it helps and if there are anything else I could help with, please let me know.