Why won't apache allow symbolic links, with SELinux?

You don't say what distro/release you are using which may be relevant. I only have Centos 6 and 7 to hand but the tools to use should be available on other distros.

The tools you should familiarise yourself with are audit2why and audit2allow.

Running your denial messages through the tools will point you in the right direction.

On the CentOS 6 sytem I have to hand the tools suggest that the current policy should allow this ( so I guess you're not using this) but that setting a particular SELinux boolean will help solve the issue.

On the CentOS 7 system I have to hand the tools suggest that setting a particular SELinux boolean will help solve theproblem.