T-Online has a simple whitelist approach, and it is usually enough to just drop them an email. I did that back in 2014, asking for my private mail server to be added to that whitelist, and I received a positive answer within a few hours.
Note that unless T-Online has additional requirements here this doesn't need to be your home address but only a valid mail address through which you can be reached.
Original German text of the law: https://www.gesetze-im-internet.de/ddg/__5.html
Google translation to English: https://www-gesetze--im--internet-de.translate.goog/ddg/__5....