If I try to 'yum remove cyrus-sasl cyrus-imapd ...' then it asks me to remove mysql postfix and so on too...
Is 'rpm -e --nodeps' the only way to remove it?
Yes, if you want to break your system. Postfix uses cyrus-sasl to do SMTP AUTH. The other dependencies are there for a reason too. Why are you trying to remove all of these packages? If you're just trying to create a minimal system or save some space, by all means remove packages you don't need but don't use --nodeps or --force or you'll break something, possibly in a very subtle way that you won't notice for some time.
Paul.