best option
yum remove exim
yum install postfix
I really don't know why anyone continues to use it. Then again, Sendmail is still everywhere, and it's even worse.
Postfix is secure by design and relatively easy to configure. Yes, there's jiggery-pokerty with SPF etc, but that happens with any MTA and if you don't understand the basic options, you shouldn't be running an MTA. And it's easy to configure for SElinux!
OpenSMTPD looks like it's worth a look as well, with perhaps a little less of a learning curve compared to Postfix (which it was obviously inspired by) for the more advanced options. But maybe a little less flexilbity overall. Haven't used it myself.