My wife replied to an e-mail and got the following error back:
<user@example.org>: host smtpin.rzone.de[2a01:238:20a:202:50f0::1097] said: 550 5.7.1 IP listed on RBL (3.0.0.127 https://www.spamhaus.org/sbl/query/SBLCSS) (in reply to RCPT TO command)
I immediately checked if my server was on blacklists. MXToolbox's blacklist check did not show any errors, and my own is-my-server-sending-too-many-mails check had not triggered.
The error message indicated that IPv6 was used, and Spamhaus's CSS FAQ says that they only list /64 subnets, and not individual IPv6 addresses - the database would simply get too large.
Now our server hoster Hosteurope only gives us a /128 block, which is a single IPv6 address. This means that another server hosted there sent spam mails, got blacklisted and now my server is punished, because we share the same /64 block :(
I contacted Hosteurope's support, but they told me that IPv6 is still in beta for them and that they could not give me my own /64 range. They also told me I should send my mail via IPv4 :(
I then configured postfix to prefer IPv4 over IPv6 (man 5 postconf):
smtp_address_preference = ipv4